3d Object paths

I have a 3d square connected at one point. It has a height of 3 squares, a width of 1 square, and length of 3 squares.

I'm supposed to find the amount of paths from S(Upper left corner), to U(bottom right corner), with no backtracking.

Then Point U is attached to the upper left corner of a cube with a width of two cubes, a height of 2 cubes, and a length of 3 cubes, with Point T in the lower right corner.

http://i14.photobucket.com/albums/a3...km/3dCubes.jpg

Thats how it looks.

I know I'm supposed to to Divide it into two parts, but thhe fact that it's a 3d object is seriously throwing me for a loop.

How do you determine the amount of paths on a 3d object(I'm assuming you have to use pascals triangle in some way)?