Hi, if you're on Team F, then you have no chance to get promoted to director. Only Team A or Team B has the chance to get promoted to director. Do you have save game before you get promoted to executive? If not, then you have to start new game.
The game has a lot of hints put in certain places. All you have to do is just pay attention to these hints. If you just skip text during dialog, then you might miss these hints.