The Morose Mononokean: Season 2 Episode 13 (S02E13)

Ashiya has spent the first seven days of high school stuck in the infirmary because of a youkai attaching itself to him. He ends up asking the owner of a small tea room called the "Mononokean" for help. This is a tale involving the very morose owner of Mononokean guiding the youkai that happened to wander into this world go to the next world.