Figure 6.1.8.7[White to move]

You see that White has two heavy pieces aimed at d8 but that the square is defended twice as well. Since one of the defenders is the king, think about forcing it back under its pawn cover where it can’t defend d8. The natural way to do this would be with a diagonal attack like 1. Bh3+. But here that move fails because Black can interpose pawns on the g and f files; and the f pawn would have protection. Yet you still should notice that White has two pieces—that same bishop and also a knight—trained on a square adjacent to Black’s king: b7. So the check 1. Bxb7+ has to be considered, as any check would be, and you see that it forces Black to play Kb8. That move changes things, of course, as d8 now is guarded just once. White mates with the usual two-against-one sacrifice: 2. Qd8+, RxQ; RxR#. The lesson is to see that there is more than one way to drive a king back from a mating square it is trying to protect. A check of any sort may do it.