Carefully is an example of what type of word?

Carefully is an adverb because it is said before doing any work. and this defines that the work must be done very watchfully or guarded . and an adverb is a word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, etc.

so careful is an adverb

The answer to your question is option a