"Her own cardigan."
Translation:Η δική της ζακέτα.
δική has the feminine nominative singular adjective ending -ή because ζακέτα is a feminine noun.
The article η is also used because that's the feminine nominative singular article and so is the one that's appropriate for the feminine noun ζακέτα.
So δικ- takes an ending that's appropriate for the gender, number, and case of the noun that follows (the possession).
So you could have τον δικό μου πατέρα, της δικής μου μητέρας, των δικών μου παιδιών, etc., with different endings depending on the gender (masculine/feminine/neuter), number (singular/plural), and case (nominative/genitive/accusative) of the noun.