We can actually see that the revised sentence that uses an adjective clause to provide additional detail is:
The ancient Greeks' search for harmony, virtue, and truth is revealed through their strict artistic conventions, which combine beauty and mathematical ratios.
Adjective clause is known as a clause that is dependent clause that acts as an adjective in a sentence. It is known as a relative clause.
An adjective clause will contain a subject and a verb.
Also, an adjective clause will begin with a relative pronoun such as which, who, whose, etc. It also answers the questions, what kind? which one? etc.
We can see that the selected revised sentence has a relative pronoun, "which" and that makes it the adjective clause that provides additional details.
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