Here's why:
* Adjective clauses modify nouns or pronouns. In this case, it modifies the implied noun "eagerness".
* Noun clauses function as nouns in a sentence. They can act as the subject, object, or complement.
Let's break down the sentence:
* How eager she was to do her best (adjective clause)
* Her eagerness (noun) was remarkable (verb phrase)
The adjective clause describes the extent of her eagerness, providing more information about the noun. It doesn't function as the subject, object, or complement of the sentence.