Question

I suggest that you dial the phone number again.

The bolded words are what kind of clause?

Answer 1

bolded words: "that you dial the phone number again."

choices:
adverb clause
adjective clause
noun clause

Answer 2

thoughts? what part of speech is the whole phrase acting as?

if you are still in doubt, consider that "suggest" is a transitive verb, with the phrase acting as its direct object