The term stems from prohibition. When the bar tender ran out of
hard alcohol, they would use a boot legged alcohol (generally grain alcohol) and cut it with a certain amount of
water. The result was an alcohol that was very close to 80 proof... 86. The slang term came to be used when the
bar ran out of alcohol they would call for the "86". Over the years the term has evolved to refer to running out of something. Although there are many theories about ladies drinks and Empire state buildings, this is historical slang term has been documented.