1995 AIME Problem 3

Starting at (0,0), an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let p be the probability that the object reaches (2,2) in six or fewer steps. Given that p can be written in the form m / n, where m and n are relatively prime positive integers, find m+n.