This time you find no pins, but if you size up the forces bearing on Black’s king you see that the bishop on a1 is poised to pin the pawn on g7 if the king can be pushed into the opposite corner. Or you consider every check for White and find two—Qh6, which is no good, and Rh8, which requires KxR in reply and places the king on a square that leaves the g7 pawn pinned. Either way you realize that h6 now is a loose square, its guard paralyzed. Threaten the king by putting a piece there: Qh6+. The king’s only flight square is g8. The queen’s next check is Qxg7#, which mates with support from the bishop on a1. Notice again how the bishop and queen usefully are coordinated. First the bishop imposes a pin that gives the queen a safe square on which to land; then the bishop provides protection as the queen chases down the king.

It was noted early that 1. Qh6+ fails. Notice precisely why: it fails because Black has 1. ...KxQ, not because Black can reply 1. ...g7xQ—for that leads to 2. Rh8#.