Answer
$14 \choose 7 $$= 3432$
Work Step by Step
To get to the final point, the rook must make 7 moves right and 7 moves up in total. All that remains is to order the moves. The number of ways to do this is $14 \choose 7$, as we can think of this as choosing 7 spots in the overall sequence to put the "up" moves, and the right moves will just fill the remaining spaces. Therefore, the answer is $14 \choose 7 $$= 3432$.