Hi,
Let R be the operation to move 1 unit right and U be the operation to move 1 unit up

Consider the path from A to B.
Moving using only right and up operations we can reach A to B in 2 ways.
Path BC: We can reach from B to C by moving 2 units right and 1 unit up in any order.
So, R,R,U can be arranged in 3!/2! = 3 ways
Path CD: We can reach from C to D by mopving 2 units right and 2 units up in any order.
So, R,R,U,U can be arranged in 4!/2!2! = 6 ways
So, number of ways from A to D though B and C is (No.of ways from A to B)*(No.of ways from B to C)*(No.of ways from C to D) = 2*3*6 = 36

Hence, C

I literally counted..but i think i could make it out

That A to B = 2
B to C = 3
C to D = 6
2*3*6

1. from A-B E-1 N-1. total 2
2. from B-C E-2 N-1. total 3
3. from C-intermediate point E-1,N-1 total 2; Intermediate-D E-1,N-1 total 2 thus C-Intermediate-D = 4
and C-D direct path E-1 N-1 total 2.

total E-D = 4+2=6

thus 2*3*6 = 36.