Answer: Transition
Explanation: I'm also taking the quiz, but i'm almost certain it is a Transitional word. Since the only time you are using the word "Eventually" is start a sentence after describing a situation where someone can't find anything.
Example: The thieves ransacked the whole house. Rummaging through drawers, and cabinets and tearing down the walls. Eventually, the noise stopped and a whooping cry of celebration sounded from outside the closet. The father and his child knew that they had found what they were looking for.