What is the possibility that 6 of my cards are double cards of continuity?

Question

I was playing a card game where I thought of the problem and could not solve. The rule is that you have to put down the bigger cards than the previous player did. The order is: 3,4,5,6,7,8,9,10,J,Q,K,A,2. The player is dealt 13 cards randomly. What is the possibility that 6 of my cards are double cards of continuity? For example: 2 Jacks, 2 Queens, and 2 Kings. They can be any cards within the deck dealt as the player can rearrange the cards to their liking later. Note: all 4 2s can't be part of the sequence as they're the biggest cards already.
Thanks!