This is an example of Permutation with repeated characters.

To go to from (0,0) (consider, southeast corner) to (8,8) (consider northwest corner) we need to take 7 Up turn and 7 right turn. It means that its a forming a string like UUUUUUURRRRRRR (Whatever the way you go, you have to take 7 Up and 7 right to reach (8,8)). Now our job is it find the how many permutation can be formed from this string. Which is a very simple task.

Total Number of permutation will be : ( factorial(14) / (factorial(7) * factorial(7))). Which is equivalent to 14C7.