Working forward from the description: the man's father has a sister, so she is his paternal aunt. The girl introduced is that aunt's daughter. Family terminology defines the child of one's parent's sibling as one's cousin, so working forward from father, to father's sister, to her daughter, lands directly on cousin without needing to test each label separately.
Checking this against the choices confirms it: the girl cannot be a daughter, since she isn't the man's own child, cannot be a niece, since that title applies to a sibling's child rather than an aunt's child, and cannot be a grand daughter, since that would need the man's own child to have a daughter.
Therefore, the correct answer is Cousin.
Another way to pin down the relationship is to identify the nearest ancestor the man and the girl have in common, and then check whether they descend through the same parent or different ones. The man's father and the girl's mother, the father's sister, are themselves siblings, so their shared parent, the man's grandfather, is the nearest common ancestor of the man and the girl. The man descends through his father's line, while the girl descends through her mother's, the aunt's, line, two different parent-lines meeting at the same grandparent.
Therefore, the correct answer is Cousin.