Restaurant lingo meaning "take an item off the menu." By extension it can also mean to get rid of almost anything (including doing away with somebody). The Urbandictionary entry attributing the term to the 1980s is erroneous. I worked as a short order cook in the late 1960s and it was in use in a half dozen NewYork city joints where I worked. Oldtimers say the term was around in the 1940s and that the derivation is Article 86 of the New York Liquor Code which describes the circumstances under which liquor should be withheld from a customer.
Restaurant manager: "we ran out of chipped beef . . . eighty-six the shit on a shingle."
To eighty-six something or someone originates in a small bar in the village. Chumley's, a prohibition era haunt for writers and artists, had two entrances: one of which was on 86 Bedford street. When the bar got raided by cops everyone would rush out of the back door on 86 Bedford.