Thanks for sharing your thoughts on what you missed! That's how you get better, by learning from your mistakes. 
I'd also like to point out that it seems to me like there's another possibility at the end. Instead of 4. Rxe6, you could play 4. Nd7+. After 4. ... Kxe7 5. Nxb8, the pawn on b4 is "poisoned" because of the threat of a fork on c6. If black discovers the danger, you can just play Rb1 and you have a terribly dangerous pawn on the queenside.
Nice puzzle. Glad that I have good eyes, that board is a little small
Thanks for sharing your thoughts on what you missed! That's how you get better, by learning from your mistakes. I'd also like to point out that it seems to me like there's another possibility at the end. Instead of 4. Rxe6, you could play 4. Nd7+. After 4. ... Kxe7 5. Nxb8, the pawn on b4 is "poisoned" because of the threat of a fork on c6. If black discovers the danger, you can just play Rb1 and you have a terribly dangerous pawn on the queenside.
Excellent point.
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Ok, so this is my first post. Hope you like it.
This position is from a game played at chess.com. I missed it while playing. Pure tactics!
So White (me) was already a Knight and a pawn ahead (a pawn at b4 that is lost). How could they icrease their advantage?
Solution commented
After 27. Nxe6+!, Black's king and (unprotected) rook are attacked (forked). Black must capture to avoid further material loss. So White gains also a destruction of Black defense (tactics again)
27. ... fxe6 28. Ra7+ Be7 This move is mandatory for Black in order to have an "escape" square. Otherwise, moving the king to h6 or h8 allows Rxh7#.
29. Rxe7+ Kf8 30 Rxe6.
So, after black plays Rbxb4, White increased their advantage by two pawn, it's attacking h7 pawn, has a passed pawn at e5.
I'm sure that if I have found this situation as a "chess problem" on a book, I would have found the solution. But I missed on a real game. I must continue practicing ....