It’s Season One, Episode 18, “Coming of Age”. You can start your search for the clip there.

While waiting, he hears an explosion nearby, and leaves the room to investigate. He finds two men trapped by fallen components in a fire-engulfed room. Wesley helps to release one man wounded under a heavy pipe, and tries to coax the other man to leave the burning room, but the man refuses. Wesley is forced to leave the scared man inside and drags the other man to safety. Outside the room, he soon realizes this was the psychological test. Eventually, the cadets are told of the results, and Mordock is granted admission into Starfleet Academy, while Wesley is encouraged to try again next year. Mordock thanks Wesley for his help and wishes him future success. After Wesley returns to the Enterprise, Picard confides in him that he also failed the examination the first time.

Thanks.