Identify the word which the italicized adverb clause modifies. john finished his work quickly after taking a break.

Adverb clause is a group of words that function as an adverb and can tell when, where, why, and how are verbs, adverbs, and adjectives. 
 
The adverb clause in this sentence is "after taking a break" and it modifies the verb quickly. It tells us when the work is done quickly.