Question

her hobby is working on the engine of her classic car.
subject
direct object
predicate nominative

Explanation:

To determine the correct term, we analyze the sentence structure. The subject is "Her hobby", the direct object would be a noun receiving the action (but here "working on...car" is a gerund phrase as a subject complement). A predicate nominative (or predicate noun) follows a linking verb ("is") and renames the subject. The gerund phrase "working on the engine of her classic car" renames "hobby", so it's a predicate nominative.

Answer:

predicate nominative