Possibly a reference to article 86 of the New York state liquor code which defines the circumstances in which a bar patron should be refused service or "86ed".
Another theory has it that this is rhyming slang for "nix." However, if so, it would be a wholly American origin, and thus would be unusual for rhyming slang.[1]
Others have suggested that this usage originated from the famous Delmonico's Restaurant in New York City, as item number 86 on their menu, their house steak, often ran out during the 19th century. However, there is no recorded usage of this term in the nineteenth century.
Another explanation is that Chumley's, which was a famous 1900s New York speakeasy, is located at 86 Bedford St. During Prohibition, an entrance through an interior adjoining courtyard was used, as it provided privacy and discretion for customers. As was a New York tradition, the cops were on the payroll of the bar and would give a ring to the bar that they were coming for a raid. The bartender would then give the command "86 everybody!", which meant that everyone should hightail it out the 86 Bedford entrance because the cops were coming in through the courtyard door.

looks like it's unclear EXACTLY where it came from