Poker Question. Can You Help?

The winning hand is two pair.  The Ace King wins the hand.  The best 5 cards are 10 10 9 9 and Ace.  Ace King has the "high card" in addition to the pair.

The flop wins the hand

In the player hand you are missing one card, but if that missing card was another ace or another king, the player would win. Any two pair would beat any one pair of any kind.

Yep, it's the best 5 card hand. So since both of the players have 2 pair (in the flop), the player with the ace would have the winning high card.