Board Thread:Support Requests - Getting Started/@comment-46539204-20200907210012/@comment-9605025-20200908035248

I assume you are talking about the legacy threaded discussion features and not the new ones based on Feeds.

A re-worked version of what has been said: Depending on the type of thread it is (article comment, blog comment, message wall, Forum), you will need to be admin/content mod/discussions mod or higher. For Forum and message wall, you can close/remove a thread if you are the one that started it. For message wall, you can close/remove a thread if it is on your wall.
 * Close - prevent new replies
 * Remove - close and hide in lists of threads
 * Lists are a user's message wall, the comments section of an article/blog, a Forum board, the "Discussion" section at the bottom of an article, or a topic page.
 * Delete (soft) - remove and hide content in threads
 * Delete (hard) - delete the actual content