You have a rook and bishop nicely coordinated against g7. The g7 pawn has got to go; if you capture it Black will not be able to recapture because your capturing piece will have protection. Indeed, you see that this position has Morphy’s mate written all over it. But do you take the pawn with your rook or with your bishop? With the rook, of course, because that’s a check; Bxg7 in this position lets Black play f7-f6 and your threat is over. (If Black’s king were on h8, you would take the pawn with your bishop because that would be the check; it would go 1. Bxg7+, Kg8; 2. Bf6+, Qg5; RxQ#.)

So you play 1. Rxg7+, which forces 1. …Kh8. Now you have another issue to consider—the one just studied: Black can interpose his f-pawn (with protection) at f6, so if you merely discover check by withdrawing your rook you will be foiled. You could try sacrificing your rook at g8 to drag Black’s king back there, but it won't work here because then you have nothing left to put on the g-file. No, this case calls for the other way of dealing with an annoying f-pawn: take it with 2. Rxf7+, going into a brief windmill pattern. Play continues 2. …Kg8; 3. Rg7+, Kh8; and now you withdraw the rook up the g-file, discovering check and mating. (Black can throw his queen or rook into the bishop’s path, but White just takes them and nothing has changed.)