The underlined part of the sentence can best be described as an adjective phrase.
In formation of sentences in English language, the words that are used usually include the following parts of speech:
An Adjective is a word that describes or modifies a noun or a pronoun. While adjective phrase is the phrase that can be used to modify or describe a noun in a sentence.
From the sentence given, extremely excited is adverbial phrase used to modify the noun vacation.
Learn more about parts of speech here:
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