"I know her cousins."

Translation: Znám její bratrance.

[OliviaSilber]

why isn't it 'jejích' as 'bratrance' is plural and masculine animated?

[Petr486191]

The form of "její" / "jijich" is derived from the person(s) whose cousins they are, not from the cousins.

her cousins -> její bratranci

his cousins -> jeho bratranci

their cousins -> jejich bratranci

[Jamie08MD]

The form "jejích" is for the genitive case (without her cousins - bez jejích bratranců); in the above sentence, you need to use the accusative case (Znám její bratrance. - both the pronoun and the noun are in the plural, masculine animate, accusative case).