I would like to run some new outlets in my garage. There is
currently a subpanel located there, the run will be fairly short. I
have a section of armored cable which was left over from work at my
office that I'd like to use. I'm thinking of using a setup which I
have seen used in other houses, but want to run past you first.

The armored cable has two 10-gauge (white & gray), 4 12-gauge
"hots" (various colors), and two 12-gauge grounds. I'd like to use
it to run 4 20-amp circuits. Circuits A and B would come off of
opposite phases, and share one of the neutrals and one of the
grounds. C and D would be run similarly. That way, neither neutral
would ever carry more than 20 amps.

I know that I would never exceed rated ampacity for any conductor,
but I do not know the NEC well enough to say whether that will meet
current code or not. Anybody want to chime in?