As the moon continues in its orbit around the earth, a part OF THE ILLUMINATED SIDE of the moon becomes visible.
The capitalized words in the above sentence represents the (2) Adjective Phrase.
Adjective Phrase is a "group" of words using an adjective, which describe the noun. For example: She has 'extremely pretty' eyes. In this sentence, extremely pretty is an adjective phrase which describing noun 'eyes'.
Adverb phrase is a "group" of words that act as adverb in a sentence. Adverb describes an adjective, verb, or another adverb. Adverb phrase is group of words which describe or modify adjective, verb, or another adverb.
In the given sentence, capitalised section “of the illuminated side” describes the noun ‘moon’. So, it is an adjective phrase.