How Many Points in Cribbage Are There Using Just These Three Cards?

My girlfriend and I were playing cribbage this weekend and she tried to get more points out of these three card then there were.

In case you've never played cribbage, one of the ways you get points is with cards in your hand that add up to 15. You score 2 points for ever 15 you have in your four card had plus a card cut from the deck that is shared as part of each players hand.

As you can see with these three cards in her hand, 7+2+6=15. Two points. Michele is new to the game of cribbage so I can't fault her for this, but I can tease her. She tried to claim she had four points because 6+2=8 and 8+7=15 for 2 points AND 7+2=9 and 9+6=15 for another 2 points.

When I told her she's using the same three cards and they can only add up to 15 one way. I had to get my friend Gary to be the decider on this, but in the end she figured it out. I ended up skunking her, meaning I reached 121 points to win the game before she got 91 points. That's worth two wins and guess what I had to explain next. She skunked me the next game so maybe I never should have told her.