When pulling a rubber band, the potential energy will be the greatest at the point of maximum elongation or stretching. This occurs when the rubber band is stretched to its maximum length before it reaches its elastic limit.
As you stretch a rubber band, you are applying force to overcome the elastic forces within the band. The potential energy of the rubber band increases as it stores the energy of this applied force. The rubber band behaves like a spring, and according to Hooke's Law, the potential energy stored in a spring is directly proportional to the amount of deformation or stretching.
At the point of maximum elongation, the potential energy is at its highest because the rubber band has been stretched the most. Once the rubber band exceeds its elastic limit, it may lose its elasticity and not return to its original shape when the force is released.