When you accept this quest, you will be transported to a large area filled with crop fields, pots, weak monsters, and a storage box. You have to pick the crops and drop them into the box (open it). Your ability to harvest is determined by your STR stat and your Gardening skill. Note that if you fulfill the quota early, leaving the quest area will nonetheless cause you to fail the quest; you have to wait for the time to run out to get your reward.