the probability that after the sixth roll the walker is back at its starting point (0, 0, 0)

A random walk on the three dimensional integer lattice is defined as follows.
The walker starts at (0, 0, 0). A standard six sided die is rolled six times. After
each roll the walker moves to one of its six nearest neighbors, according to the
following protocol: if the die rolls 1, 2, 3, 4, 5, or 6 dots the walker jumps one
unit in the +x, −x, +y, −y,z, −z direction respectively.
Find the probability that after the sixth roll the walker is back at its starting
point (0, 0, 0)