In this video, the teacher explains the importance of a memorable closing in a letter and provides three possible ways to end a letter: using a plea for action, telling a story that supports your opinion, or stating why your thinking matters. The teacher cautions against simply stating the last piece of evidence and not drafting a closing paragraph, as it can be boring and forgettable. The teacher then guides the viewers through three steps to write a memorable closing: thinking of a story that illustrates the thesis, using the story to write the closing paragraph, and restating the thesis.