First, I'm going to highlight all the adverbs in the options:
A. Lucy quickly hid behind the tree.
B. Mr. Dodge moved in an extremely slow manner.
C. Jacob was a very smart boy.
D. The dress was terribly old
Adverbs can modify verbs or adjectives, and in options B, C and D it is adjectives that are modified: slow, smart, old.
The correct answer is A: in option A the adverb modifies a verb
