Learn Spanish (Latin America): Vamos a la playa con mis toallas y las de mi amiga. - We are going to the beach with my towels and my friend's.

English uses an apostrophe-'s' to show possession, but Spanish uses the word de (of). To say "my friend's [towels]" without repeating the word for towels, we use a definite article + de. Because toallas is feminine and plural, we use the feminine plural article las. So, las de mi amiga literally translates to "the ones of my friend."

Why does the sentence use mis toallas but mi amiga?

In Spanish, possessive adjectives like "my" must match the noun they describe in number (singular or plural). Since toallas (towels) is plural, you must use the plural mis. Since amiga (friend) is singular, you use the singular mi. They change to match the items or people being talked about, not the speaker who owns them!

Could I say vamos en la playa to mean we are going to the beach?

No, you need to use a (to). The verb ir (to go) describes movement toward a destination, so it is almost always followed by a to show direction. You use en (in/at/on) to describe being located somewhere without movement, like estamos en la playa (we are at the beach).