In the 3-dimensional lattice; how many ways are there to go from the origin (0, 0, 0) to the point (6, 2, 4); when in a step starting from a point (x, y, z); I can move to (x + 1, y, z), to (x, y + 1, z) or (x, y, z + 1)?

Twelve movements must occur.

Ways from (0, 0, 0) to (6, 2, 4) = 12! / (6! 2! 4!).

No other tricks to my answer?