It's a little confusing " white to move, you are black"!
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You can't do anything because it's white to move. If it was black to move then I would probably do Bg4.
You are Black. You must stop fxg6.
I don't see how you can stop fxg6, since white can't even play fxg6, his f-pawn is still on f2 and there is no piece on g6 square to be captured. Doesn't even work if you mirror the coordinates. So I'll assume that you meant knight on f6. I don't think there is any way to prevent white from playing Nxf6 or Bxf6... Be6 doesn't do much. And whatever you do, in case of capturing on f6 there is no other choice but to recapture with g pawn.
I've been using a few bishop sacs successfully lately, so I guess I'd go with 1...Bxf2+, 2. Kxf2 and then 2...Ng4+. But it's just an idea and (of course) white does not need to reply Kxf2, although it does lose the ability to castle altogether.
That doesn't work because bishop on g5 is protected by knight on f3, so you lose a bishop for a pawn because you can't capture on g5 with your queen to get the bishop back. Also, after Ng4+, then white king moves, then you have to either move the queen away because she's under attack or you have to move your knight back to f6 (blocking the attack) - and that is the best move, cause otherwise white will play h3 and kick your knight back to f6 one move later anyway. So, this still doesn't prevent capture on f6 and recapture by g-pawn.
Kh8. There's no way to stop the g-file from being opened so might as well get your king off it and put your rook on it. If White doesn't take on f6, then provoke it with Nd7. You'll get useful doubled f-pawns that you can use to attack White's center and a semi-open g-file to attack down.
Raweyes and Paranoid good answer so you both get a trophy each! But there is two trophy still to be everybody!
But why would you want to stop gxf6? I'd rather have that pawn on f6! Otherwise this position is too boring and I'd fall asleep and lose the game on time! In fact I'd even say that Black is better after Kh1, Nxf6 gxf6, Bh6 Rg8! Those pawns are easily un-double-able and Black will have the more active pieces.
The most convenient way to stop Bgxf6 is to just move the knight away, the opponent will have "only" 6 point advantage. Maybe you have in mind Legal's mate, but in this position such mate is not possible.
Legals Mate will be stopped by Kf1
Exactly. Legal's mate would only work if f1 would be blocked by another white piece and if white knight wouldn't be on f3. I thought you are one of those legal-mate forum posters at first.
I myself don't think there is any way to stop Bxf6. Can you tell us the solution so we can see if there's anything wrong with it?
Who gets the the two trophies?