White has a bishop check with Bd6+. How would Black respond? Probably with Ka8. Whenever you imagine a move that would force your opponent to move—and especially a move that would force him to move his king—imagine the position that would result and interrogate it with the same questions you might ask if it were the board in front of you. What Black pieces would be loose? What pieces are aligned? Black's queen and rook—which indeed are already aligned from the start, and would then be forkable with Bc7. Since the queen is one of the targets, naturally we look to make sure the bishop will have protection. It will, from the rook at c4.

This description suggests how looking at every check might have led to the fork. Another way to see it, though, is to step back and notice first Black’s queen and rook on the same diagonal, especially since they have no pieces between them. That pattern is a set up for a double attack by the bishop. The question then becomes whether you might maneuver the bishop into position, since it cannot get to c7 directly. When you want to make a preliminary move without giving your opponent time to defend against the fork you are creating, the preliminary move has to be forcing. A check is best. Conveniently, White’s bishop can give a check on the way to c7 by stopping first at d6.