Question on Outs/Statistics...

I was asked this question and am not sure what he correct answer is.

In an all-in heads up situation...You are behind (and have been behind from the start) after the turn. What is the most possible outs you could have (not being eliminated..I guess a chop would be included) and what is an example. I was thinking something like you: open-ended straight flush draw with over cards against an opponent with a lower pair where neither card is of the suit that I'm holding...but I don't know...can anyone think of scenario with more outs?

22 v KcQc on JcTcTs8s board

Supposedly the answer is 44outs

a guy that was close guessed..."I have 22, opponent has 23 - board is 2 pr like 6688 - 44 outs. "

the persom that asked the question said that he was right about the number of outs, but he would have to be behind all the way. SO, his 22 against 23 is wrong. The board is also wrong.

Can anyone figure this out?

You have 23
Opp has 24
Board is XXYY (no 2s/3s/4s). You chop on anything but 2 or 4 = 5 anti-outs. 52 - 8 = 44.

Oh, and fold pre-flop.