Final answer:
The client is demonstrating the defense mechanism of displacement, where they transferred their anger onto working out at the gym instead of confronting their boss directly.
Step-by-step explanation:
The defense mechanism that the client is demonstrating is displacement. Displacement is the process of transferring inappropriate urges or behaviors onto a more acceptable or less threatening target. In this scenario, the client was angry at their boss for accusing them of stealing, but instead of confronting their boss directly, they channeled their anger and frustration into working out at the gym. By doing so, they redirected their emotions from the original source of anger to a safer outlet.