On my daughters LT80, if I grab the rear grab handle and move it side to side, there is significant amount of play within the rear shock. I also notice that this movement translates all the way up to the front of the engine mounts. I looked to see if there is any bushings that are bad on the rear shock but didn't notice anything. What is the problem?

 

Tighten the front motor mount bolt(s). Should do it.