The sentence that contains an adverb modifying another adverb is: "My brother sings loudly in the shower."
In this sentence, "loudly" is the adverb modifying the verb "sings." However, here it was mentioned in conjunction with the requirement of identifying an adverb modifying an adverb, which is not present in the options provided. If you're looking for an example of an adverb modifying another adverb, that would typically include a sentence such as "She runs very quickly," where "very" modifies the adverb "quickly."
In the given options, none of the sentences fit that specific criterion exactly. However, "carefully" in the first sentence does modify the adjective "work," if considering the broader context of how adverbs operate.