When would a bouncy ball have the most potential energy

At the peak of its bounce.

Step-by-step explanation:

When a bouncing ball hits the floor, most of its kinetic energy is converted into elastic potential energy. This is energy that is stored in the ball as it deforms when it hits the floor

When the ball resumes its shape and bounces back, the elastic potential energy is converted into kinetic energy and gravitational potential energy.

While the ball is in the air, KE + PE = constant.

As the ball rises, its kinetic energy decreases and its gravitational potential energy increases.

At the very peak of its bounce, KE = 0 and all the energy is gravitational PE.

The ball has the maximum potential energy at the peak of its bounce.