“Eighty-six” is diner slang for taking an item off the menu or canceling an order. It’s also used by bars and restaurants when they refuse to serve an unruly or drunk customer. By extension, it can mean rejecting, discarding, or getting rid of anything or anyone (especially gangster style).
No telling where the term really originated. Some sources say it was a rhyme for “nix.” Others say it came from Article 86 of the New York Liquor Code. Perhaps the best story points to Chumley’s, a prohibition era bar in Greenwich Village. The place had a back door that exited at 86 Bedford Street — and when the bar got raided, everyone made a dash for it. (“Quick! Eighty-six it!”)
Example (as used by Michael Masterson today): “Instead of being happy to get information about a new marketing technique he could profit from, my client was using his considerable intellectual energy to eighty-six it.”