Are you referring to a chess mentor lesson or a video? Can you provide the link so we cab see the position you're talking about?
Minor Pieces v. Rooks, a good middle/endgame lesson, a commentary

Yeaha Spiel, here it goed, http://www.chess.com/chessmentor/view_lesson?id=559
This was a really great lesson, ranked at 1800 elo, when you achieve correctly, which is why I was trying to glean as much about principles as I could from this lesson. But the better move by black was take the pawn on his third rank, don't wait, but this makes the mate impossible I feel, based on the method taught in this lesson, though which is instructional in some principles anyway.

Nice lesson indeed!
At which point does the computer capture c6?
I've only looked at the direct end which leeds to an imediate mate, see variation.

hey dude, its instead of 2..Qa5, the computer has the move, at medium level ~1400, Rxc6. then the ending does not quite work out in favor of white, but at least in the way the lesson teaches that a mate can be reached.
This is a really great lesson, that I have reviewed many times, in which both rooks are sacrificed to get to control the diagonals with the bishops. Just one comment, I was interested in expanding so I clicked on play vs. the computer, and I found quickly that the computer erased my advantage conveyed in the lesson by the single move Rxc6 pawn. With this move, the computer took a better root than the player in the tournament, and I was not able to beat the computer using the strategy that the lesson conveyed. The whole game shifted with that one move, and i can't see that a win could have been made by white after that countermove. The computer's move, sacrificing his/her own rook, was able to remove the edge that the GM had used to get to mate in the original game, and by finding it, I also increased I feel, my ability to think defensively. But yes, this move took out the possibility of a passed white pawn, which was the crown of the mate, had the pawn on c6 not been taken. Please consider..