Final answer:
Arthur faces the conflict of having to prove he is Uther's child.
Step-by-step explanation:
The conflict that Arthur faces, according to the selection, is that he has to show he is Uther's child. This conflict arises because Arthur is the rightful heir to the throne, but there are doubts about his parentage. To prove his legitimacy, he must demonstrate his connection to his father, Uther Pendragon.
The legend of King Arthur often encompasses various challenges that Arthur must overcome to establish his legitimacy and authority. This particular conflict is a central theme in many stories about Arthur, where proving his lineage is crucial for his recognition as the king and for gaining the loyalty of his subjects.