Learn Italian: Mi piacciono le tue labbra.

Labbra (lips) is a special irregular plural. The singular word is actually masculine: il labbro (the lip). But when it becomes plural, it changes to feminine and takes the unusual ending -a to become le labbra. Several body parts in Italian do this, such as il braccio (the arm) becoming le braccia.

Since the singular is masculine and the plural is feminine, how do I know which possessive word to use?

You always match the possessive word to the gender and number of the noun exactly as it is used in the sentence. Since labbra is feminine and plural, the article and possessive must be feminine and plural too, which gives us le tue.

Why do we use piacciono here instead of piace?

The verb piacere works backwards compared to English. You are literally saying that your lips are pleasing to me. Because the subject doing the pleasing (le tue labbra) is plural, the verb must be in the plural form: piacciono. If you were talking about a single lip, it would be Mi piace il tuo labbro.

Why do we need the article le before tue labbra? Don't we sometimes drop the article with possessives?