Right away you (as Black) should notice your two bishops raking White’s kingside position, and your interest especially should be piqued by the way the light-squared bishop penetrates all the way to h1. You also have a rook on h8. The question is how to use these resources. (a) You need to open the h-file so that you can get pressure going vertically as well as diagonally. (b) Bxg3 is one natural idea, hoping to draw White’s h-pawn over to the g-file as it recaptures and thus allow you to play Rh1#. But White can recapture with his f-pawn instead, ruining everything (for then his queen protects h2). (c) So try taking out the h-pawn directly with your rook: Rxh2. If White plays KxR, Black has an open file and diagonal and is ready to mate. He needs to get a fresh piece onto the h-file and has two ways to do it, both of which are fine: Qh6+ or Rh8+. White’s king is forced to g1, and now Black mates with a heavy piece on h1.

It always is important to ask what happens if your opponent declines to accept your sacrifices. Here you start with Rxh2, to which White doesn’t have to reply KxR. True, he is threatened with Rh1#, but he has another way to address this. He can block the diagonal by interposing a pawn: f2-f3. The pawn is protected twice, so this does frustrate Black’s mate threat; but by opening the second rank it allows Black to play RxQ for nothing. (Black also ends up with an eventual forced mate; he has too much unanswered firepower directed at the White king’s position. But it is enough for now to see the big material gain.) A lesson: when you size up a risk that your opponent will interpose a pawn, carefully examine the side consequences and especially any lines that the pawn move will open.