White has an attack on the black king. White has the bishop's pair. Black must close the position. 1...h5 is imperative to both stop the attack and restrain the bishops.
Position Study and Thinking Critique

Very nice and concise. My problem is figuring out move order. If i may ask you a direct question, what are your thoughts on why h5 needs to come before Nxd3+ specifically?
the main problem i had with 1..h5 right away is that white could move the ls bishop and retain the bishop pair and it was hard for me to determine if that should be allowed.
BLACK TO MOVE
Above is the position I was given to select the best move. Below is my thought process:
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first impression: white is slightly better. activity, bishop pair, attacking chances
material count: even
king safety: black is slightly better. castled with queens still on vs exposed in center
pawn structure: black might be slightly better due to whites doubled pawns.
piece imbalances: bishop pair and knight vs knights and ls bishop
weaknesses: e3 or f3 or e5 pawn depending. might be weaknesses in the long term for white. the h-file might be a weakness for black in the short term giving white attacking chances.
who is better with queens off the board: closer to equal with queens off as whites attacking chances are reduced
whose position is easier to play: white becuase they have more space
WHOSE POSITION IS STATICALLY BETTER? material 0, imbalance 0.1, pawns -0.1, knights -0.1, bishops 0.1, rooks 0.1, queens 0, king -0.1, threats 0.1, passed 0, mobility/space 0.15. TOTAL +0.25
ARE ALL YOUR PIECES DEFENDED? h6 might be a concern
CHECKS, CAPTURES, THREATS? nxd3+, hxg, nxe5
move ideas: hxg would threaten the bishop. nxd3+ would get rid of the bishop pair and could even be followed by h5 to lock down the kingside or 1..nxd3+ 2.qxd3 nc5 followed by hxg and looks like black is solving mobility problems and has weaknesses to attack. d5 tries to undermine the bs bishop and make the pawns weaker. i think what i want to go for are the moves nxd3, hxg, and d5. move order is important though. the other idea is nxe5 to lure the bishop to e5 and activate the queen. haven't found a line for that idea though.
continuations: 1..nxd3+ 2.qxd3 nc5 looks good for black as the knight is within striking distance of the b2 pawn and checking the king at any moment 2.cxd3 hxg looks kind of miserable though. 1..d5 is too unclear. 1..hxg seems too soon. i think hxg comes after. the best line seems to be 1..nxd3+ 2.cxd3 h5 and black will finish developement and play for long term while white doesn't seem to have an attack any more.
CANDIDATE MOVE: 1.Nxd3+
IS THE MOVE SAFE? Yes, because it is a forcing move.
After 1..nxd3+ 2.cxd3 h5 black can play c5 and looks really good. white doesn't seem to really have a pawn break and has weaknesses. I think black has more than equalized and is now favored.
WHOSE POSITION IS BETTER AFTER THE MOVE? -0.3
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Please tell me how you would go about analyzing this position given that you have unlimited time. I'm not really interested in engine lines. Trying to improve my organic thinking by opening it to critique.
Thank you in advance!