Folding this preflop, when someone 3bets UTG they rep strong hands and defending 67s OOP here is not something we want, we will get into tough spots postflop like this one.
As played I'll probably call here because we picked up a double gutshot and we have fd already

As 67s is probably the worst hand you open from EP you definitely shouldn't defend against a 3bet from the button, I would sometimes defend this hand if I have position postflop(depends on the opponents 3bet % too).
Check calling the flop is ok because you have enough outs but I would probably check raise to something like $2.5 . Reason for that is so you fold out his overcards like AK, AQ, AJ and KQ that don't also have a flush draw. The reason I don't like check calling so much is because you too often find yourself in a weird situation like this one. I'd probably raise flop and get it in on the turn to get as much fold equity as possible. But the main problem in this hand is that you defend against a 3bet too wide and get in sticky situations like this, even when you flop great you still aren't too sure what you are supposed to do. Some better players could tell you something different but that's my view on it. Hope it helps.

The main issue here is the preflop defend. Definitely way too wide to be calling OOP preflop.

Flop play is fine. I'd usually just check/call, but there are certainly merits to a check/raise on this kind of texture.

I don't bother bluffing the turn too much at these limits, but 6c7c I would be check-shipping. It can sometimes be hard to check/call draws profitably OOP given the river situation that ensues. Having said that, would be pretty crazy to lay down a combo draw here, and we probably have some fold equity at the very least.

I agree. In retrospective and usually the defend is too wide. In that case I decided to call, as Villain had a pretty high 3bet % from the BTN and he was a little bit fishier.

I am not opening 76s too often from UTG. It maybe happens once every 5-10 times i get dealt that hand UTG. But I guess thats the punishment for playing it. Having a really nice draw board on the flop but no cards that help on the turn

For sure way to wide pre flop and will even fall into a pre flop fold in some players books.

Post flop check raise the flop and bomb it off or get it in. We will get A high flop floats to fold turn and have high equity vs most hands.

I think fold before the flop is best move, on flop i think bet line is check raise and push any turn, and as played you must call, you got 30% equity.