Why do this problem?
The context is interesting and this can be an exercise in finding distances using coordinates. This process, of repeatedly reflecting the snooker table in its sides, occurs in many areas of advanced mathematics and for a simple introduction see the article In Space Do All Roads Lead Home?

Possible approach
Use the hint.

Key question
We know the ball bounces of the cushion at an equal angle so how do we use this fact to find the right point on the cushion to aim for?

Possible support
See Snookered.