The correct option is D that he will not give up - object
A noun clause is a dependent clause that functions as a noun. It usually begins with what, whatever, whom, that. A noun clause can act as a subject, object, predicate nominative or object of a preposition, in a sentence.
The words "that he will not give up" is a noun clause because it begins with the pronoun 'that', it has a subject 'he' and a verb 'will not give up'; 'will not' is the modal/helping verb and 'give up' is the main verb. The noun clause functions as the object of the verb "said" in the given sentence. Hence option B is correct.
Option A is incorrect because it isn't a noun clause, it contains the main verb "said" and noun clauses do not contain the main verb.
The subject performs the action of the verb and the object receives that action, they do not include the verb. The subject, verb, and object are separate parts of a sentence.
Option C is incorrect because 'not give up' is not a clause, it does not have a subject.
Option D is incorrect because it contains fragments of the entire sentence.