How is mate guaranteed - Bobby Fischer 134 I am working through Bobby Fischer Teaches Chess and #134 asks

If White plays Rook-takes-Rook-check, can he mate?

The answer is Yes, the mate is delivered by the white Queen.  However, can't it be prevented?
Here's the board:
[title &quot;Bobby Fischer #134&quot;]
[fen &quot;1r1r2k1/6pp/2n4q/2p1p2Q/pp2N2P/5P2/PPPR2P1/1K1R4 w - - 0 1&quot;]

I can see how to get mate, with the Queen: 1. Rxd8 Rxd8 2. Rxd8 Nxd8 3. Qe8  for mate.
However, if 1. Rxd8 Nxd8 2. Rxd8 Rxd8 .  This prevents the Qe8 mate, doesn't it?
So when the question asks &quot;can he mate&quot;, yes but it's not guaranteed.  Do I understand the board correctly?
However, if black takes with Rook, then Knight takes' white's rook,
white rook to take knight, then black rook to take white rook. This
prevents the Qe8 mate, doesn't it?

No, it accelerates it. Let's look at what happens if black takes with the knight instead of the rook
[fen &quot;1r1r2k1/6pp/2n4q/2p1p2Q/pp2N2P/5P2/PPPR2P1/1K1R4 w - - 0 1&quot;]

1. Rxd8 Nxd8 2. Qe8# {oops!}

Black gets checkmated in 2 moves instead of 3