This one is harder. Black has just played his knight to e3, attacking the rook on f1 and the pawn on g2 (for the third time). White’s instinctive response might be defensive: move the rook to safety. But by now you know to ask first whether you might take the initiative and inflict damage with checks or captures of your own. Perhaps you notice that Black’s knight is aligned vertically with one of his rooks and diagonally with another. The knight and both rooks all are protected, so a skewer doesn’t quite work yet; but an exchange can change the picture markedly, so experiment. The only capture for White to consider is RxN. Black replies RxR. Now you see that Black’s two rooks would be left aligned on a diagonal with no pawns on the line—a pattern that invites a skewer by your bishop if it can be arranged. The trouble is that the bishop cannot safely get onto the rooks’ line from where it now sits; if it moves to g5 it gets captured. The challenge: maneuver the bishop onto that line, and with threats that give the enemy no time to avoid the emerging skewer. The solution: plot a course to h6 for the bishop that allows it to give check along the way. First Bg7+, with protection from the rook on g3; then Bxh6 after Black moves his king. Now the bishop attacks both rooks and will take one of them.
Or rather all that is the idea. Before putting it into motion think carefully about the move order, for in this position it makes a great difference:
(a) Suppose White starts with RxN, expecting RxR and setting the stage for the skewer by leaving the rooks aligned. He will be in for a nasty surprise: Black ignores the loss of his knight, plays Rxg2+, and mates in two more moves (White’s king is forced to h1; Black plays Rxh2, then moves his other rook to g2 on the next move, ending the game). Lesson: don’t take for granted that your opponent’s reply to a capture is forced, especially when he has threats against your king. He may be able to ignore the capture and go for mate or threaten some other terrible result.
(b) Now suppose instead that White starts with Bg7+, forcing Ke7; then White immediately plays Bxh6, expecting to play RxN next move. Well, but Black simply replies to Bxh6 with NxR. The problem is that White’s Bxh6 isn’t a check; it gives the initiative back to Black. Again, every step of White’s sequence needs to be forced to ensure success.
(c) So the right sequence is to start with 1. Bg7+, Ke7—then to play RxN+ back at White’s end of the board, since that move now is a check (remember that Black’s king would now be on the e-file!). Black would be forced to deal with the check by playing RxR, and now the pieces at last are arranged for the skewer Bxh6. Two checks, then a skewer: that’s what makes it work, as the checks keep White in firm control of the action. (By the way, if Black replies to Bg7+ with Kg8, he of course walks his king into the discovered check Bxh6+, which White follows next move with BxN, winning a whole piece.)
The skewer described in the main line here (sequence (c), above) costs White a bishop and a rook and gains him a knight, a rook, and a pawn. But apart from winning a pawn it also defuses a bothersome threat Black was building with three pieces in the White king’s neighborhood. The best defense is a good offense.