Learn Russian: Девочка не любит смотреть на себя в зеркало. - The girl does not like to look at herself in the mirror.

It is in the accusative case. The verb смотреть (to look) paired with the preposition на (at) requires the accusative case for the object being looked at. Because the action reflects back to the subject (the girl), it translates to herself in English.

Why do we use the preposition на before себя?

In Russian, the standard phrase for looking at something is смотреть на. You cannot just put себя directly after the verb; it needs the preposition на to show what the gaze is directed at.

Could I use её instead of себя in this sentence?

If you said на её, it would mean the girl does not like looking at a completely different female person. To show that the subject (the girl) is looking at her own reflection, you must use the reflexive pronoun себя.

Why is it в зеркало (accusative) instead of в зеркале (prepositional)?

When you look into a mirror, Russian treats your gaze as a movement directed toward a target, so it uses the accusative case (в зеркало). If you used the prepositional case (в зеркале), it would literally imply the girl is physically located inside the mirror while not liking to look at herself!