— - Since your condition: (If 8direction is moving and Down arrow or Up Arrow is down) is only setting animations when down or up arrow is pressed then it will not run animations when left or right key is pressed. Is that the problem because since I can't see the animations or the other events then that is the only possible explanation I can come up with.
I suggest adding :
*If Player is moving and
*******************Right Arrow is pressed then
---------------------------------> Set animation to "RunningRight"
*******************Left Arrow is pressed then
---------------------------------> Set animation to "RunningLeft"