Answer:
The correct answer is Object of the Preposition
Explanation:
A noun clause is a dependent clause that can act like a noun in a sentence. It could function as the subject, object of a preposition, appositive, subject complement, direct, and indirect object.
The object of the preposition is the pronoun, noun, or noun phrase that comes after a preposition in a sentence.
In the sentence given, the noun clause is; "whomever he meets". The pronoun, "he" comes after the preposition, "whomever". Therefore, it is its object.