An inspection of your checks and their aftermath turns up 1. RxN+, KxR. The important point to see about the king’s new position is that it is trapped on the back rank by the White pawn on b6. And Black’s back rank is bereft of defenders. This means White probably mates if he can get a heavy piece onto the back rank—which in turn means that Black’s f6 pawn is pinned, since if it moves off the f-file White has Rf8+ and then mates after Black tries useless interpositions with his queen and rook. The natural way to take advantage of a pinned pawn is by capturing something it protects, which White does with QxR+—and now Black cannot avoid some version of the mate just described. The net of this is that White wins a piece, since if Black sees all this coming he will reply to the initial RxN+ by moving his king rather than recapturing with it.
The key idea in this position is that if Black’s king moves to b8, his pawn on f6 suddenly is pinned to his back rank. This is hard to see at first because it seems strange to think of a pawn being pinned to an empty square. These positions thus present an important general idea to contemplate: if you can manage to get the enemy king trapped on the back rank, notice that this may turn your heavy pieces into monsters—and pin whatever enemy pawns or pieces block their path.