e6 is the best move here coz it allows you to break black's pawn structure as you guessed it right. As the pawn moves from e5 to e6, it frees up e5 square for your knight/bishop. Also, it weakens black's g6 pawn. However, I must point out that do not make the mistake of moving your knight/bishop to e5 right after black captures fxe6. If you play Ne5 or Be5, black's knight can capture your piece on e5 and after you play Bxd7+, the same knight on e5 can swing back to d7 square. Hence, black saves his knight and white loses a piece.
Why sacrifice on e6?
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Just curious why a pawn sacrifice on e6 is suggested here? I'm guessing it has something to do with black's pawn structure, but I'm not sure exactly how.