The mating threats considered so far all have involved a attack by the queen on a square already attacked by another piece—typically a bishop. That is the most common sort of mating threat to use as part of a queen fork, but there are others as well; here we'll consider a few examples. Many of them involve an initial move to set up the fork (a check, capture, or threat) followed by a double attack that includes a mating threat. Like the studies toward the end of the chapter on knight forks, they require a willingness to play with the consequences of various checks and captures, always asking about the next check that would be available and looking for familiar patterns to emerge.
Start with the position on the left. Scan for loose Black material and you find the rook at c5 (and the queen; but focus on the rook). White has no way to attack it and give check at the same time, but do not give up; study the Black king’s position carefully. What are the constraints on its movement, and what are its resulting vulnerabilities? It is stuck on the back rank with no defenders there. If White’s queen or rook were to land on the back rank, it would be mate. So the back rank itself becomes a target in just the way that a loose piece would be; White’s goal is to attack the Black rook and the back rank at the same time. What move threatens both? Qb4, winning the rook after Black fends off the threat of Qb8+ (and QxQ# after Black interposes his queen) with a move like h7-h6.