"How many pets did her family have?"
Translation:Hvor mange kjæledyr hadde familien hennes?
But 'familien' isn't what 'sin' refers to, but a 'she'.
"familien hennes" = "the family of hers"
"familien sin" = "the family's own"
From Possesive's Tips and Notes:
Sin, Si, Sitt, & Sine
The above are an interesting set of possessive adjectives in Norwegian. They all translate to his, her, its, or their and can only be attached to objects in a sentence. Sin, Si, Sitt, & Sine describe something that the subject has or owns, not somebody else. This distinction does not exist in English.