Learn Croatian: Doplivala je do obale pune ljudi. - She swam up to the shore full of people.

The prefix do- adds the meaning of reaching a destination or a limit. While the base verb plivati describes the ongoing action of swimming, doplivati is a perfective verb that specifically means to reach a goal by swimming or to swim up to a certain point.

Is it normal to use the preposition do right after a verb that already starts with the do- prefix?

Yes, this is a very common Croatian pattern. When a verb uses the prefix do- to show movement toward a boundary, it is frequently followed by the matching preposition do (meaning up to) to explicitly introduce that destination, which in this case is obale.

Why is the adjective pune in the genitive case?

It modifies the noun obala (shore). Because the preposition do requires its object to be in the genitive case, obala becomes obale. The adjective must match its noun in gender, number, and case, so it becomes the feminine singular genitive pune.

Why is the word ljudi also in the genitive case here?

The adjective pun (full) always requires the noun following it to be in the genitive case, expressing what something is full of. Here, ljudi is the genitive plural form, meaning of people.