Never heard of it so I had to look
https://www.merriam-webster.com/wordplay/eighty-six-meaning-origin
Eighty-six is slang meaning "to throw out," "to get rid of," or "to refuse service to." It comes from 1930s soda-counter slang meaning that an item was sold out. There is varying anecdotal evidence about why the term eighty-six was used, but the most common theory is that it is rhyming slang for nix.