complex 00 geometry

A step starting at a point P in the XY -plane consists of moving by one unit from P in one of three directions: directly to the right or in the direction of one of the two rays that make the angle of ±120 with positive X-axis. (An opposite move, i.e. to the left/southeast/northeast, is not allowed.) A path consists of a number of such steps, each new step starting where the previous step ended. Points and steps in a path may repeat. Find the number of paths starting at (1,0) and ending at (2,0) that consist of exactly 6 steps