M0 Week 4 Challenge Q20

The question is:
and what I thought was, because it's a 3x3 rectangle, to get from A to B, you'd need to go right 3 times and go down 3 times (regardless of the order). if the third row wasn't missing a segment, then the answer would be 6 choose 3 which is 20. but since there is a missing segment then my fourth move (there are six moves in total) couldn't be a go right but instead a go down. and so the number of paths would decrease by half, which is 10.
and yet clearly, this is not the case. could anyone explain why my solution failed? thanks!!!