Figure[White to move]

Again Black’s king seems to have breathing room, so a back rank mate doesn’t come to mind right away; but that freedom of movement can disappear in a hurry. Notice that if White plays Qc6 his queen cuts off the king's flight squares to the left and right (b7 and d7) just as the pawn did in the previous study. This should cause you to look for heavy pieces that would be able to descend to the eighth rank, and thus find the threat of Ra8#. To avoid that outcome Black has to play QxQ—but now White recaptures using his d5 pawn, which ends up on c6 and again seals off b7 and d7. This time Black’s only way of avoiding Ra8# is to move his king to b8 where it can defend a8 itself. But then White plays his other rook from f1 to a1, giving the rook on a7 some backup. He will mate next move no matter what Black does.

Again, the lesson is to notice how advanced pieces and pawns can abruptly trap the king on the back rank and allow it to be mated there. A piece on the sixth rank that seals off squares on the seventh can be mighty powerful.