Now let's combine some guard-removal themes. The crucial thing here is to see all of White’s possible mating ideas: Re8 almost does it; Qf8 almost does it; so does Qg8, or QxBf6—probably the easiest of the ideas to overlook. The problem is that in every case the needed square has protection; indeed, in every case the protection is provided by Black’s queen. When the queen gives you so much trouble, your instinct should be to experiment with moves like Re8+—a flush attack.
Black has no choice but to take out the rook and two ways he can do it. The first is QxR, in which case the queen has been drawn away from the protection of f6; White mates there with his queen. (On this view of the position Black’s problem was that his queen was overworked, trying to guard too many mating squares.) Black’s second possibility for a reply to Re8+ is BxR. This creates a different problem for him: he has put his bishop between his queen and mating squares it was supposed to protect. Now White mates with Qf8 or Qg8. It becomes a case of interference.
Black had no way to avoid mate by the time White reached this position, but there still is a defensive lesson to be learned: anytime your king is stuck on the back rank and you are forced to make a capture there, be mindful of how it will affect the king’s defenses: the movement of your pieces might affect your ability to fend off a mating attack by blocking the protection you are able to provide along the rank.