In a logic puzzle like this, it is usually easiest to mark impossible combinations with Xs and circle correct ones. There are multiple ways to use the clues to find the correct answer. One possible solving path follows:
Since the bathroom was swept, we know the living room was not. Since the living room also was not dusted or polished, it must have been organized.
Since either Charlie or Jordan worked in the bathroom, Avery did not. Since Avery also was not in the dining room or kitchen, they must have cleaned the living room.
Avery worked in the living room, and the living room was organized. Therefore, Avery did the organizing.
Neither Charlie or Jordan were in the Dining Room. Since Avery also wasn’t, Riley must have done the chore there.
Avery was organizing and Jordan was polishing. That means either Charlie or Riley did the sweeping. Since we are told that the bathroom was swept, and Riley worked in the dining room, that means that Charlie mush have swept the bathroom.
By process of elimination, Riley must have dusted the dining room, and Jordan must have polished in the kitchen.
The answers associated with the correct letters, when read from top to bottom, spell ANSWER RAKING, giving as the answer a chore nobody yet completed, RAKING.