The question this time is whether White can mate. He has the telltale combination of a rook and queen aimed at f7, suggesting a mating sequence that would start with Qxf7+. If Black plays his king to h8, White mates immediately with Qxg7 (a queen and rook on the seventh rank are fearsome). So Black is unlikely to do that, and will instead play RxQ. Carefully assess what comes next. White has two rooks on the d-file, so Rd8+ suggests itself. Black can reply either with the capture RxR or with the interposition Rf8:
(a) If Black plays RxR, White follows up immediately with RxR+, getting mileage out of his doubled rooks. Now Black would be forced to interpose with Rf8. This might look secure, but when you see that the f8 rook would be defended just by its king you should think about ways to drive the king back, as with Bc4+. This forces Kh8, and now RxR is checkmate.
(b) If Black instead replies to Rd8+ by interposing with Rf8 right away, however, the analysis is crucially different. Black still has two rooks on the back rank and White has no effective way to use his two rooks against them. He still can use his bishop to push Black’s king to h8, but then RxRf8 is met by Black with RxRf8. So the mate fails, and the initial move Qxf7+ should not be played.
The important moral is to be careful in thinking through each of your opponent’s possible replies. If any of them work you mustn’t go forward in hopes that he will make a mistake. Assume he will play his best move. Keeping all the possible replies straight can be tricky, of course, but when your moves are checks it is less difficult. Just be thorough then in asking whether he has a capture, or an interposition, or must move his king—for those are his only three options in reply.