Question

Which sentence contains an adverb clause?
a. Sandy, who is never hopeful, didn't think Mom's plan was going to work.
b. She planned to piece the shreds together and repair the book.
c. When we go to the store, we might have to buy Billy a new book.
d. Mom is someone who always looks on the bright side.

Answer 1

An adverb clause has essentially the same function as an adverb. "When" in c is key to it being an adverb clause.

Answer 2

An adverb clause is a subtype of subordinate/dependent clauses, meaning that it cannot exist on its own, outside of the main, independent clause. In these examples, there are several dependent clauses, in A, C, and D, however, only in C there is an adverb clause 'when we go to the store'. 
In the other examples, there are only adjective clauses.
So, the correct answer is C.