Just to be clear, we're holding J-6-6-2-2 (suits irrelevant), and the board is:
J 10 8 J 10 (live)
3 4 7 Q K (dead)
Hero and 4 opponents are still in the hand, with 4, 2, 2, and 2 cards left.
We are locked out of the low and probably splitting the high if anyone is going high. There's a nonzero chance we're outright losing the high too, though with a Q and K dead, only 10-10 and A-A-A in the hole beat us now, plus a chance of A-A or A-J in the hole spiking an ace on the river.
What else is giving action on the high? Maybe a really drunk 10, but in reality, probably nothing. If we've been checked to by everyone on the turn, I can see a small and not really compelling argument for betting (maybe we are ahead and should protect our hand) and checking through (because if the action gets pushed now it's a really gross spot).
I know it looks like the "nut boat," but this hand is less than top pair top kicker on the turn in Hold'em. Especially against a whole field. You will usually either win a little or lose a big fraction of your stack.