Here's why:
* Adverbs modify verbs, adjectives, or other adverbs. They tell us *how*, *when*, *where*, *to what extent*, or *why* something happens.
* "Coarsely" describes the manner in which something is done. For example: "He spoke coarsely about his opponent." (How did he speak? Coarsely.)
Let me know if you'd like more examples!