It is potential energy because the band is not in movement, th band has the potential to move.
I assume that the ball is stationary (v=0) at point B, so its total energy is just potential energy, and it is equal to 7.35 J.
At point A, all this energy has converted into kinetic energy, which is:

And since K=7.35 J, we can find the velocity, v:
I am pretty sure it’s A
The cue exerts force onto the white ball which pushes the blue ball into the direction of the hole.