In reference to having killed someone, how did the term "I 86'd him" come about?

In American English, the number 86 used as a verb, to "eighty-six," means to "ignore" or "get rid of". The first recorded usage of this term occurs in the mid-1930s. There are many theories of the origin of this usage, most pertain either to death or to prohibition.

All these explanations are associated with a specific origin, but there is another which would seem to have a universality which on one hand makes it a plausible origin, but on the other hand may be too simple to be true; the dimensions of a grave hole being dug to 8' by 6'. This has a problem though in the standard dimensions being a lot closer to 7' by 6'.

https://en.wikipedia.org/wiki/86_(number)#American_slang

Eighty-six, slang for "eliminate" (1936), originated as lunch counter slang, a cook's word for "none" when asked for something not available, probably rhyming slang for nix.

http://www.etymonline.com/index.php?search=eighty-six&searchmode=none

One explanation for the term derives from the observation deck on the 86th floor of the Empire State Building. A popular suicide point at one time.
http://www.urbandictionary.com/define.php?term=86ed

Here are a number of other theories as to how this expression developed:

http://www.foodreference.com/html/art86.html