Eight.
There are eight hands that have your hand beat at this moment in time. In all of the following hands the suit of the cards does not matter because no flush possibilities figure into this situation therefore the hands are considered suit neutral. Your opponent could have trips with pocket Fives, pocket Sixes or pocket Eights (3 hands). They could have two pair if they hold 56, 58 or 68 (3 hands). They could also hold 47 or 79 to give them a straight (2 hands). Therefore the total is 8 (3 + 3 + 2 = 8).
I’ll credit the account shortly @OmaNutz