Answer:
I believe the underlined part is "that he won't go."
In this case, it is a "noun clause."
Explanation:
A "noun clause" is a dependent clause in a sentence. It acts as a noun, thus the name noun clause. In the sentence above, the noun clause is "that he won't go." This acts as an object of the verb "says."
Remember that a noun clause has a "subject" and a "verb." It is easy to spot a noun clause by taking note of the following words: that, what, where, why, whom, whomever, whatever, whether, etc.
