How many ways are there to go from A to D, passing through

First of all, the question is definitely not 'this simple'. Though once you know how to deal with such questions, it becomes quite easy.

I do agree with vicksikand. Its easy to solve it his way. Let me elaborate on the theory behind it.

When I want to go from A to B, I have to take 1 step north and 1 step east. I can do this in two ways: First north, then east or first east, then north. I can say that I have two steps N and E and I have to arrange them. I can do it in 2 ways (NE) or (EN).

When I want to go from B to C, I have to take 1 step north and 2 steps east. I can do it in three ways: First north, then east, then east (NEE) or First east, then north, then east (ENE) or first east, then east, then north (EEN).
I can say I have 3 steps NEE and I have to arrange these in different ways. It can be done in 3!/2! ways = 3 ways (We divide by 2! because we have 2 E's. For more details check permutations theory)

When I want to go from C to D, we need to take two steps north and two east. That is, we have to arrange NNEE is different ways. This can be done in 4!/2!*2! = 6 ways (NNEE) or (NENE) or (NEEN) or (EENN) or (ENEN) or (ENNE)
We divide by two 2! because N is twice and E is twice.

Total number of ways of going from A to D = 2*3*6 = 36