My game with Big4at

I was told that he made his move but I can't locate game to make my move

You only appeared to have three games going when I checked, but none with Big4at.
One of the games shows it is not started.

Did you create open invite games?
If so perhaps one of those games was picked up by Big4at, and then deleted shortly after that. A game can be deleted by either player before the third move is made.
When someone takes up one of your open invite games you receive an email message telling you who has accepted the game.
If they then delete the game it will be returned to the open invite page for someone else to pick up.

Maybe that's what happened.

<EDIT> I just did a search for Big4at and could not find any member with that username.