Many cultures have stories about a hero who goes on a quest such as Hercules, King Arthur, and Gilgamesh. What could carl jung say this exemplified

In my opinion, Jung would say this exemplified an archetype. According to him, archetypes are universal, symbolic patterns in humanity's collective unconsciousness, which are not acquired through experience but are inherited by being born into the human race. Going on a dangerous and risky quest would be an archetype because it symbolizes initiation into manhood, which every boy has to undertake upon reaching a certain age.