Learn Danish: Hun vil gerne leve op til sine forældres forventninger. - She wants to live up to her parents' expectations.

The word sine is a reflexive possessive pronoun. It refers back to the subject of the sentence, Hun (She). Because she is trying to live up to her own parents, we must use sine (which is the plural form for forældre). If we used hendes, it would mean she wants to live up to some other woman's parents' expectations.

Does the phrase leve op til translate directly to the English live up to?

Yes, it translates perfectly! The phrase at leve op til is a common Danish expression that functions exactly the same way as the English phrase: to meet certain standards or expectations.

Could I just say Hun vil leve op til instead of Hun vil gerne leve op til?

You could, but adding gerne makes it sound much more natural here. While vil means wants to or will, adding gerne translates closer to would very much like to. It shows a willing, internal desire rather than just a simple statement of fact or a future action.

Why doesn't forældres have an apostrophe for the possessive form?

In Danish, you show possession by adding an -s to the end of the noun, but you do not use an apostrophe before the -s. So the plural noun forældre (parents) simply becomes forældres (parents') without any extra punctuation.