Final answer:
The bolded noun clause 'whoever had scratched up the side of his car' functions as the direct object in the given sentence, as it is the receiver of the action of the verb 'find'.
Step-by-step explanation:
The bolded noun clause in the sentence 'Michael was determined to find whoever had scratched up the side of his car' is functioning as the direct object of the verb 'find'. In this sentence, Michael is the subject wanting to identify the person responsible for the damage. The noun clause 'whoever had scratched up the side of his car' is what Michael wants to find, which makes it the receiver of the action and therefore the direct object.