"I know her cousins."
Translation:Znám její bratrance.
why isn't it 'jejích' as 'bratrance' is plural and masculine animated?
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
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).