The answers are incomplete for they do not explain why sometimes the wheels turn forward and sometimes backward and why that changes with the speed.
If an object (picture) is displayed at two different positions in space one shortly after the other then (depending upon time and distance) the object (picture) is perceived to have moved from one position to the other (thats's why we can see motion with 24 stable frames per second). The perceived movement is into the direction of the second presentation. If an object (picture) is first displayed in one position and then in two position opposite to the first position it is perceived to move to the second position nearer to the first one. With the spokes, there are two choices from one film frame to the next, clockwise is a spoke and counterclockwise as well. To which spoke will the eye perceive the 'old' spoke to have moved? To that nearer to the old position. If that is clockwise and the coach moves from left to right or if that is counterclockwise and the coach moves from right to left then a forward motion of the wheels will be seen. in the other two cases a backward motion will be seen.
One can also have the perception of motion both clockwise and counterclockwise motion though nothing at all changes in the picture: