This one is harder. White starts with his rook pinning Black’s bishop. The bishop is attacked once, by White’s rook, and guarded once, by Black’s king. The king is a weak guardian because if it is attacked it very often has to move; it can’t just be protected. The sight of Black’s king and the pinned bishop flush up next to each other thus should get you thinking about ways to loosen the bishop by driving the king away. Here White can use a check for the purpose: he plays Rxg7+; Black replies KxR; and now the bishop is loose, allowing RxB. But this trades a rook for a bishop and a pawn—not a great deal. Can it be improved? Yes. White precedes the above sequence with f2-f4. Consideration of this move by White is compulsory; you always ask whether you can attack a pinned piece with a pawn. Here Black would answer with Rxf4. This is interesting, for it leaves the rook attacked once by White’s king and protected once by Black’s bishop—which is the pinned piece, and is about to be lost. Now White plays Rxg7. After Black plays KxR and White plays RxB+, Black has to spend a move avoiding the check; and this gives White time to take Black’s rook with his king. It’s a classic use of the priority of check. In effect that initial move f2-f4, and the capture of the pawn by Black, gave White a kicker to play at the end of the sequence that made the whole thing worthwhile.
This position illustrates in simple form how a check can drag the king away from a pinned piece that it is supposed to be guarding. The more challenging lesson is to see the importance of considering every way of attacking the pinned piece and the consequences that would follow from it. At first blush f2-f4 looks futile because of Rxf4, but on closer examination this is seen to leave the rook vulnerable to capture.