If you try to accept Teacher Plushes Adventurer introduction on a full inventory the quest just bugs out completely and doesn't allow you to accept it afterwards since the quest prior to it gives you an item and since your inventory is full you can't accept it and it just closes the window then you try to talk to him again and you can't. Only option is to delete your character, wait 11 hours and make sure your inventory is empty.
hope to stay here for awhile.