Many cultures have stories about a hero who goes on a quest, such as hercules, king arthur, and gilgamesh. what would carl jung say this exemplified?

The answer is Archetypes. Jung at first worked with kindred psychoanalyst Sigmund Freud, whose 1899 work The Interpretation of Dreams had connected essentialness to the repeating topics and themes in individuals' fantasies and tried to comprehend their importance to subjects' minds and their mental prosperity.