"The girl likes her cups."
Translation:Jenta liker koppene sine.
No: 'sine' here implies that the subject, the girl, owns the cups, and not some other girl/woman. Were 'hennes' to be used it would imply that the subject didn't own the cups, but some other girl/woman.
Jenta liker koppene sine. = The girl likes her own cups.
Jenta liker koppene hennes. = The girl likes the cups of someone else.