White has to kill all of the large black dragon (from D7 to Q18), only getting half isn't enough. You can safely assume that, because of the large eye, black will win all capturing races. Black also has sufficient local ko threats (even at the end) to be alive in ko.
White has no need to play out the squeeze at the top starting with white N17 so it isn't included in any variations. Also no variations are included where white plays H18 and black can retake at H17 (it'll be obvious what I mean when you get to the relevant part of the problem).
Advice:
Play thickly - Don't give black extra forcing moves, stay connected where possible, make eye shape.
Spoil black's eye-shape (duh!).
Keep an eye on your liberties.
(;SZ[19]AB[rl]AB[es]AB[er]AB[dq]AB[cq]AB[br]AB[cp]AB[bp]AB[bo]AB[bn]AB[cn]AB[cm]AB[dm]AB[em]AB[fn]AB[fo]AB[fp]AB[ep]AB[gp]AB[hp]AB[ip]AB[fl]AB[fk]AB[fj]AB[gj]AB[ej]AB[dj]AB[cj]AB[ch]AB[dh]AB[df]AB[cf]AB[ce]AB[cd]AB[cc]AB[cb]AB[db]AB[eb]AB[ea]AB[fa]AB[gb]AB[hc]AB[ib]AB[ia]AB[ja]AB[lb]AB[la]AB[ma]AB[na]AB[pa]AB[pb]AB[ob]AB[pc]AB[qd]AB[qe]AB[pe]AB[pf]AB[od]AB[nd]AB[qg]AB[qh]AB[qi]AB[qj]AB[rk]AB[og]AB[oh]AB[oi]AB[nh]AB[mh]AB[mi]AB[kh]AB[kf]AB[je]AB[kd]AB[ji]AB[ih]AB[hh]AB[gh]AB[hi]AB[ij]AB[kj]AB[ik]AB[il]AB[hl]AB[im]AB[km]AB[kk]AB[ll]AB[lm]AB[nl]AB[nm]AB[om]AB[pn]AB[qm]AB[qo]AB[no]AB[jq]AB[kq]AB[lq]AB[pq]AB[pr]AB[ak]AB[kb]AB[kg]AB[lh]AW[do]AW[gn]AW[jr]AW[kr]AW[iq]AW[hq]AW[gq]AW[fq]AW[eq]AW[fr]AW[fs]AW[dr]AW[cs]AW[mq]AW[nr]AW[np]AW[lo]AW[jo]AW[jp]AW[in]AW[ho]AW[go]AW[hm]AW[gm]AW[gl]AW[gk]AW[hk]AW[hj]AW[lk]AW[mk]AW[ml]AW[mm]AW[nk]AW[nj]AW[ni]AW[ol]AW[pm]AW[pk]AW[qk]AW[pj]AW[pi]AW[ph]AW[pg]AW[rh]AW[rg]AW[rf]AW[qf]AW[re]AW[rd]AW[qc]AW[qb]AW[qa]AW[mb]AW[nb]AW[nc]AW[md]AW[ne]AW[oe]AW[of]AW[lc]AW[kc]AW[jc]AW[jb]AW[ic]AW[ie]AW[jf]AW[jh]AW[hg]AW[gg]AW[gi]AW[fi]AW[ei]AW[fg]AW[ef]AW[ge]AW[ed]AW[ec]AW[fc]AW[fb]AW[gc]AW[ca]AW[ba]AW[bb]AW[bc]AW[bd]AW[be]AW[bh]AW[aj]AW[bj]AW[ck]AW[dk]AW[cl]AW[al]AW[am]AW[bm]AW[an]AW[ao]AW[ap]AW[aq]AW[bq]AW[mg]AW[lg]C[White to kill the dragon completely. Hint: White starts with a thick defensive move on the left.]FF[4]GM[1]AP[Jago:Version 4.18]GN[templd14a2]
(;W[bk];B[bg]
(;W[bf];B[hd]
(;W[id];B[ee]
(;W[ff];B[pd]
(;W[le];B[ko]C[Black needs to try some trickery now, stay on your toes.]
(;W[kp];B[ln]
(;W[lp];B[rj]
(;W[nn];B[pl]
(;W[mn];B[oo];W[mo];B[fe]C[Please resist the temptation to atari at F16, I haven't included any variations and its bad style.]
(;W[gd];B[ke]
(;W[he];B[ha]
(;W[ng];B[ld]
(;W[lf]C[RIGHT])
(;W[mf]C[RIGHT])
(;W[me]C[RIGHT]))
(;W[mf];B[ng])
(;W[lf];B[nf];W[me];B[ng]))
(;W[ng];B[mf]
(;W[lf];B[ld]
(;W[me]C[black is unable to push at H15 to falsify the eye due to shortage of liberties. RIGHT])
(;W[he];B[me];W[hb];B[ga]))
(;W[he];B[me];W[hb];B[ga]))
(;W[lf];B[nf]
(;W[me];B[ng])
(;W[he];B[ha];W[me];B[ng]))
(;W[mf];B[ng];W[he];B[ha]))
(;W[he];B[hb];W[ga];B[gd]C[white can capture the Q16 stones but black lives]))
(;W[on];B[ok];W[oj];B[oo]))
(;W[mn];B[oj]
(;W[ok];B[mo];W[nn];B[oo];W[on];B[ql])
(;W[nn];B[ok];W[on];B[pl])))
(;W[kn];B[mo]
(;W[rj];B[io]
(;W[jn];B[fm];W[hn];B[lp]C[ko])
(;W[hn];B[fm];W[jn];B[lp]C[ko]))
(;W[lp];B[rj])
(;W[mp];B[rj])
(;W[nn];B[io]
(;W[jn];B[fm];W[hn];B[lp]C[ko])
(;W[hn];B[fm];W[jn];B[lp]C[ko]))
(;W[mn];B[io]
(;W[jn];B[fm];W[hn];B[lp]C[ko])
(;W[hn];B[fm];W[jn];B[lp]C[ko])))
(;W[rj];B[io]
(;W[kn];B[fm])
(;W[jn];B[fm];W[hn];B[lp];W[kn];B[jm]))
(;W[nn];B[io]
(;W[jn];B[fm];W[hn];B[lp];W[kn];B[jm])
(;W[kn];B[fm]))
(;W[mn];B[io]
(;W[jn];B[fm];W[hn];B[lp];W[kn];B[jm])
(;W[kn];B[fm]))
(;W[jn];B[mo]
(;W[lp];B[rj])
(;W[kn];B[rj]))
(;W[mo];B[io]
(;W[jn];B[fm];W[hn];B[lp]
(;W[mp];B[mn];W[rj];B[fe]C[Please reist the temptation to play atari at F16. I haven't included any variations and its bad style.]
(;W[gd];B[ke]
(;W[ng];B[mf]
(;W[lf];B[ld]
(;W[me]C[Black can't play H15 to falsify the eye due to shortage of liberties. RIGHT])
(;W[he];B[me];W[hb];B[ga]))
(;W[he];B[me];W[hb];B[ga]))
(;W[he];B[ha]
(;W[ng];B[ld]
(;W[lf]C[RIGHT])
(;W[mf]C[RIGHT])
(;W[me]C[RIGHT]))
(;W[mf];B[ng])
(;W[lf];B[nf];W[me];B[ng]))
(;W[mf];B[ng])
(;W[lf];B[nf];W[me];B[ng]))
(;W[he];B[hb];W[ga];B[gd]C[white can take the Q16 stones but black is alive]))
(;W[kn];B[mn];W[rj];B[jm])
(;W[lr];B[mn];W[mp];B[rj]))
(;W[kn];B[fm]))
(;W[mp];B[mo]
(;W[lp];B[rj])
(;W[kn];B[rj])))
(;W[kn];B[ln]
(;W[kp];B[io]
(;W[jn];B[fm];W[hn];B[mo];W[rj];B[lp]C[ko])
(;W[hn];B[fm];W[jn];B[mo];W[rj];B[lp]C[ko]))
(;W[lp];B[jn])
(;W[jn];B[mo]
(;W[lp];B[rj])
(;W[kp];B[rj]))
(;W[mo];B[jn])
(;W[mp];B[mo]
(;W[lp];B[rj])
(;W[kp];B[rj]))
(;W[rj];B[jn])
(;W[io];B[mo]
(;W[kp];B[rj])
(;W[lp];B[rj]))
(;W[mn];B[jn]))
(;W[lp];B[jn]
(;W[io];B[kp])
(;W[kp];B[io]))
(;W[jn];B[ln]
(;W[rj];B[mo];W[lp];B[kp])
(;W[mn];B[mo];W[lp];B[kp])
(;W[mo];B[mn];W[rj];B[kp])
(;W[kp];B[mo]
(;W[lp];B[rj])
(;W[kn];B[rj])
(;))
(;W[kn];B[mo]
(;W[lp];B[rj])
(;W[kp];B[rj]))
(;W[lp];B[mo];W[rj];B[kp])
(;W[nn];B[mo];W[lp];B[kp]))
(;W[ln];B[io]
(;W[jn];B[fm];W[hn];B[kn])
(;W[kn];B[fm])))
(;W[me];B[fe]C[Please resist the temptation to atari at F16, no variations are included and its bad style.]
(;W[gd];B[le]
(;W[he];B[ha];W[ng];B[mf])
(;W[ng];B[mf];W[he];B[ha]))
(;W[he];B[le]
(;W[ng];B[mf])
(;W[gd];B[ha];W[ng];B[mf]))
(;W[ng];B[gd];W[fd];B[de];W[he];B[hb];W[ga]C[white can capture the Q16 stones but black is alive]))
(;W[mf];B[le];W[me];B[fe]C[Please resist the temptation to atari at F16, no variations are included and its bad style.]
(;W[gd];B[ng];W[he];B[ha])
(;W[he];B[ng];W[gd];B[ha])
(;W[ng];B[gd];W[fd];B[de];W[he];B[hb];W[ga];B[dc]C[white can capture the Q16 stones but black is alive]))
(;W[nf];B[le];W[me];B[fe]C[white is dead]))
(;W[fe];B[eg]
(;W[ff];B[fh])
(;W[fh];B[ff]C[black has his second eye at D13 or D15]))
(;W[eg];B[fe]
(;W[gd];B[pd]
(;W[le];B[ke]
(;W[ng];B[mf]
(;W[lf];B[if]
(;W[he];B[ha]
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[he];B[me]
(;W[hb];B[ga];W[lf];B[ld])
(;W[lf];B[ld];W[hb];B[ga])))
(;W[he];B[ha]
(;W[ng];B[mf];W[lf];B[if]
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[mf];B[ng])
(;W[ff];B[nf];W[me];B[ng])
(;W[ig];B[nf];W[me];B[ng])
(;W[if];B[nf];W[me];B[ng])
(;W[lf];B[nf];W[me];B[ng]))
(;W[lf];B[nf];W[me];B[ng])
(;W[mf];B[ng])
(;W[ff];B[nf];W[me];B[ng])
(;W[ig];B[nf];W[me];B[ng])
(;W[if];B[nf];W[me];B[ng]))
(;W[me]C[white dies in gote - he has half an eye at O14 and another half near H14])
(;W[mf];B[le];W[me]C[white dies in gote - he has half an eye at O14 and another half near H14])
(;W[he];B[me];W[hb];B[ga]))
(;W[he];B[hb];W[ga];B[gd]C[black lives - NB - he could have killed the whole white group in a capturing race after playing Q16 instead of H18, but this refutation is simpler.]))
(;W[fh];B[fe]
(;W[gd];B[pd]
(;W[le];B[ke]
(;W[he];B[ha]
(;W[ng];B[mf]
(;W[lf];B[if]
(;W[ff];B[hf])
(;W[hf];B[ff]))
(;))
(;W[mf];B[ng])
(;W[lf];B[nf];W[me];B[ng])
(;W[if];B[nf];W[me];B[ng])
(;W[ff];B[nf];W[me];B[ng])
(;W[ig];B[nf];W[me];B[ng]))
(;W[ng];B[mf]
(;W[lf];B[if]
(;W[he];B[ha]
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[he];B[me]
(;W[hb];B[ga])
(;W[lf];B[ld];W[hb];B[ga])))
(;W[if];B[nf];W[me];B[ng])
(;W[ig];B[nf];W[me];B[ng])
(;W[ff];B[nf];W[me];B[ng])
(;W[mf];B[ng])
(;W[lf];B[nf];W[me];B[ng]))
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[mf];B[le];W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[he];B[me];W[hb];B[ga]))
(;W[he];B[hb];W[ga];B[gd]C[black lives - note black could have killed the whole white group in a capturing race by playing Q16 instead of H18, but this refutation is simpler.]))
(;W[pd];B[eg]
(;W[ff];B[fh])
(;W[fh];B[ff])))
(;W[he];B[id]
(;W[jd];B[ke]
(;W[gd];B[hb];W[ga];B[fe];W[ee];B[if]
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[ff];B[pd]
(;W[gd];B[hb]
(;W[ga];B[me])
(;W[me];B[ga]))
(;W[me];B[ga]))
(;W[pd];B[fe]
(;W[gd];B[hb];W[ga];B[ee])
(;W[ee];B[if]
(;W[ff];B[hf])
(;W[hf];B[ff])
(;W[gd];B[hb])))
(;W[if];B[pd]
(;W[me];B[ga])
(;W[gd];B[hb]
(;W[me];B[ga])
(;W[ga];B[me])))
(;W[ee];B[pd]
(;W[me];B[ga])
(;W[gd];B[hb]
(;W[me];B[ga])
(;W[ga];B[me])))
(;W[fe];B[pd]
(;W[me];B[ga])
(;W[gd];B[hb]
(;W[ga];B[me])
(;W[me];B[ga]))))
(;W[le];B[jd]))
(;W[jd];B[ke]
(;W[id];B[ee]
(;W[ff];B[pd]
(;W[le];B[fe]C[Please resist the temptation to atari at F16, I haven't included any variations and its bad style.]
(;W[gd];B[nf]
(;W[me];B[ng];W[he];B[ha])
(;W[he];B[ha];W[me];B[ng]))
(;W[he];B[nf]
(;W[me];B[ng])
(;W[gd];B[ha];W[me];B[ng])))
(;W[me];B[fe]C[white dies - there is half an eye at O14 and another half eye near H14])
(;W[mf];B[le];W[me];B[fe]C[white dies - there is half an eye at O14 and another half eye near H14]))
(;W[eg];B[fe]
(;W[gd];B[pd]
(;W[le];B[nf];W[me];B[ng])
(;W[he];B[ha]
(;W[le]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[mf];B[le];W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14]))
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[mf];B[le]
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[he];B[ha];W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])))
(;W[he];B[pd]
(;W[le]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[mf];B[le]
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[gd];B[ha];W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14]))
(;W[gd];B[ha]
(;W[le]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[mf];B[le];W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14]))))
(;W[fh];B[fe]
(;W[gd];B[pd]
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[le]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[mf];B[le]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[he];B[ha]
(;W[le]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[mf]C[white dies in gote - there is half an eye at O14 and another half eye near H14])))
(;W[he];B[pd]
(;W[le]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[me]C[white dies in gote - there is half an eye at O14 and another half eye near H14])
(;W[mf]C[white dies in gote - there is half an eye at O14 and another half eye near H14])))
(;W[fe];B[eg]
(;W[ff];B[fh])
(;W[fh];B[ff]C[black has a second eye at D13 or D15]))
(;W[pd];B[eg]
(;W[ff];B[fh])
(;W[fh];B[ff])))
(;W[he];B[id]C[Please see variations where white plays at H15 in response to black H16 for how this fails.]
(;W[gd];B[hb];W[ga];B[fe];W[ee];B[if]
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[ff];B[pd]
(;W[gd];B[hb]
(;W[ga];B[me])
(;W[me];B[ga]))
(;W[me];B[ga]))
(;W[pd];B[fe]
(;W[gd];B[hb];W[ga];B[ee])
(;W[ee];B[if]
(;W[ff];B[hf])
(;W[hf];B[ff])
(;W[gd];B[hb])))
(;W[if];B[pd]
(;W[me];B[ga])
(;W[gd];B[hb]
(;W[me];B[ga])
(;W[ga];B[me])))
(;W[ee];B[pd]
(;W[me];B[ga])
(;W[gd];B[hb]
(;W[me];B[ga])
(;W[ga];B[me])))
(;W[fe];B[pd]
(;W[me];B[ga])
(;W[gd];B[hb]
(;W[ga];B[me])
(;W[me];B[ga]))))
(;W[gd];B[id]C[Please see variations where white responds to H16 at G16 for how this fails.]
(;W[pd];B[fe]
(;W[he];B[hb];W[ga];B[ee])
(;W[ee];B[if];W[he];B[hb]))
(;W[he];B[hb];W[ga];B[fe];W[ee];B[if]
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[fe];B[pd]
(;W[me];B[ga])
(;W[he];B[hb]
(;W[me];B[ga])
(;W[ga];B[me])))))
(;W[gd];B[id]
(;W[jd];B[ke]
(;W[pd];B[fe]
(;W[he];B[hb];W[ga];B[ee])
(;W[ee];B[if];W[he];B[hb]))
(;W[he];B[hb];W[ga];B[fe];W[ee];B[if]
(;W[hf];B[ff])
(;W[ff];B[hf]))
(;W[fe];B[pd]
(;W[me];B[ga])
(;W[he];B[hb]
(;W[me];B[ga])
(;W[ga];B[me]))))
(;W[le];B[if]))
(;W[pd];B[id];W[jd];B[ke]
(;W[fe];B[gd];W[he];B[if])
(;W[gd];B[fe]
(;W[he];B[hb];W[ga];B[ee])
(;W[ee];B[if];W[he];B[hb]))
(;W[he];B[fe]
(;W[ee];B[if]
(;W[hf];B[ff])
(;W[ff];B[hf])
(;W[gd];B[hb]))
(;W[gd];B[hb];W[ga];B[ee]))))
(;W[bi];B[bf])
(;W[ag];B[bi]
(;W[ah];B[af];W[ai];B[bf])
(;W[ai];B[eh];W[fh];B[bf]))
(;W[ah];B[bf])
(;W[dg];B[bi];W[ah];B[ag];W[ai];B[eh]
(;W[fh];B[eg])
(;W[eg];B[cg];W[fh];B[ae];W[ad];B[ab])
(;W[ci];B[fh]))
(;W[eg];B[bf];W[dg];B[ae]C[white only catches half of black's group]))
(;W[cr];B[bg]
(;W[ah];B[bf])
(;W[bi];B[bf])
(;W[bf];B[bi];W[ah];B[ag])
(;W[dg];B[bi];W[ah];B[ag])
(;W[eg];B[bi];W[ah];B[ag])
(;W[ag];B[bi]
(;W[ah];B[af])
(;W[ai];B[eh]
(;W[fh];B[bf])
(;W[ci];B[fh]))))
(;W[ar];B[bg]
(;W[ah];B[bf])
(;W[bi];B[bf])
(;W[bf];B[bi];W[ah];B[ag])
(;W[dg];B[bi];W[ah];B[ag])
(;W[eg];B[bi];W[ah];B[ag])
(;W[ag];B[bi]
(;W[ah];B[af])
(;W[ai];B[eh]
(;W[fh];B[bf])
(;W[ci];B[fh]))))
(;W[bg];B[ar]
(;W[bk];B[bs])
(;W[bl];B[bs]))
(;W[bf];B[ar]
(;W[bk];B[bs])
(;W[bl];B[bs]))
(;W[bi];B[ar]
(;W[bk];B[bs])
(;W[bl];B[bs]))
(;W[fm];B[io]))