"This chair is hers."
Translation:Η καρέκλα αυτή είναι δική της.
Greek requires the definite article with demonstrative pronouns used as adjectives, e.g., αυτό το αγόρι, "this boy," αυτό το μήλο, "this apple." (Also with possessive pronouns, e.g., το άλογο μου, "my horse," ο σκύλος του, "his dog"). There was a section on it in DL that you can go back to for a refresher.
There are a few mistakes unfortunately.
δίκη = court trial
δική = her (possessive), her own
Αυτή είναι η καρέκλα = This is the chair
Αυτή η καρέκλα = This chair
η καρέκλα δική της wrong word order
η δική της καρέκλα = her own chair
... είναι δική της. = ... is hers.
Greek syntax is more flexible than English syntax, but there are still limitations as to how words are grouped together and what order they can go in. :)