Answer
$6$
Work Step by Step
This is very similar to the problem in part (a) R means moving to the right, and D means going down. We are going from start to finish in 6 steps, we need to take 5 steps to the right and 1 down.
We are looking for a 6 four-letter sequence that contain only letters R and D with D occurring only once, therefore we choose where D will be, that is 6 choices, and then the other letters are R's. So there are 6 six-letter sequences that contain only letters R and D with D occurring only once