Why is Qg4-Qe6 the correct move here? Given this board setup:

6k1/1p3rpp/1q1p4/p2Pp3/P5Q1/1P3PP1/2R3KP/8 w - - 3 13


Puzzle states: White to move, find the best move. The puzzle solution says Qg4-e6 and the rationale is that Rc2-c8+ cannot be stopped.  It seems to me, and some computer programs agree, that going directly for Rc2-c8+ is better because it forces a response of Qb6-d8 followed by Rc8xd8+ Rf7-f8, Qg4-e6+ Kg8-h8, Rd8xf8#. I am no master, I barely can call myself novice. So why is the solution saying that Qg4-e6 is better?
You're absolutely right. Qe6 only seems to draw:

6k1/1p3rpp/1q1p4/p2Pp3/P5Q1/1P3PP1/2R3KP/8 w - - 3 13

1. Qe6 g6 2. Rc8 Kg7


There's no forced win for white here as far as I can see.