Why should I expect that black moves Rxd2 after I move Bxe3 in this puzzle? I've been playing a few puzzles for a couple of days, and I see that often the final move to chessmate is easy to spot, but earlier moves aren't (to me).
In this case, for instance, why should I expect black to defend the king with the rook, rather than, say, eating it with the queen?
4rk2/1bq2p1Q/3p1bp1/1p1n2N1/4PB2/2Pp3P/1P1N4/4RK1 w - - 0 2

1. Bxd6 Re7 2. Qxf7
The point here is that none of Black's possible responses to 1. Bxd6 prevent 2. Qxf7#. Blocking with the rook or queen leaves it pinned, and blocking with the knight or bishop or capturing with the queen means that the black queen is no longer attacking f7. The puzzle just gives an example second move, with the implication that it doesn't matter which one they pick. (The fact that this example involves a pin makes 2. Qxf7 a little bit less obvious, so that's probably the motivation for that choice.)