Well you are always looking for a forcing move in puzzles. Firstly I was looking at moving the Nd6 somewhere to uncover an attack on the black queen by the Bf4. The problem is that the Bf4 is undefended so any knight move eg. Nxf7 is answered by Qxf4 so OK you win the rook on d8 but it's not a checkmate or anything...so other forcing moves - Rxg7...it's always a flag that a move might be dangerous and work tactically if the king has to recapture and step out. Must it recapture though or can black play something else because it's not check? The thing is, black hardly has any useful moves at all...Nd5 maybe or Qa5 perhaps, but these can both be met by Bxh6 and mate is threatened immediately by retreating the rook eg. Rg3#. Just about any other black move will give away material so Kxg7 has to be played really. Aside from this, in terms of a puzzle it doesn't really matter that something else can be played which is also losing - if none of the knight moves work then there are no other direct forcing moves for white other than Rxg7.
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Stop trying to think like an engine and return to humanity. As a human you ought to be extremely happy capturing Pg7 for free which opens new attack lines to the black king besides gaining a pawn. Once you verified that black cannot take the rook without losing his queen you simply continue playing chess on the level where you are and you have a good chance of winning the game. Chess does not consist of calculating M9s and M10s per the engines but of playing solid preferrably simple chess moves to build on an advantage you achieved. Black will collapse when you merely avoid playing stupid moves.
Found this puzzle in a beginners book. Was hoping someone had some ideas about how White would know that Black had to capture on the second move. After doing some engine analysis on the position, I can see that capturing is correct, but it seems like the lines where Black choses not to capture are pretty complicated... frequently leading to M9 or M10 positions. Definitely beyond anything a beginner would see.
I want to be able to get these sorts of puzzles right in the future, so how would you guys go about solving this? The drawbacks of not capturing just wouldn't be clear to me at my level, but the importance of capturing is what makes the whole tactic work.