Question

How many ways are there to move from one corner of a cube to the diagonally opposite corner, in three moves, each of which travels along one edge of the cube?

Answer 1

looks like 6 to me
there are 3 ways to make the first move.
Then from the new corner, there are 2 ways to continue.
Then there is a single last move.

Answer 2

Yes, and you have to multiply to get the answer.