4 left. Not sure what action is correct here. I don't hate my play but I am not sure if it's correct.

PokerStars No-Limit Hold'em Tourney, Big Blind is t150 (4 handed) Poker Stars Converter Tool from FlopTurnRiver.com (Format: FCP)

Hero (t1698)
UTG (t6147)
Button (t2325)
SB (t3330)

Preflop: Hero is BB with 6 , 6 .
UTG calls t150, 2 folds, Hero checks.

Flop: (t375) 9 , 8 , 7 (2 players)

Final Pot: t375

I'm first to act. Lead the flop? Check/Raise? Check/Call? Check/Fold

Or should I have shoved preflop as the short stack?

I would shove pre, you're hand has a lot of value but is tricky to play after the flop, and allthough UTG is the bigstack, his move is very weak and there's probably a big gap between what he's limping with PF and what he'll call a shove with.

C-bet, shove to a re-raise

I think the reason this situation is tough is because none of your options are horrible.

If you shove, villain may fold and you pick up the blinds. Villain may call with a wide range of hands you're flipping against. This isn't bad either.

Some opponents, with a big stack UTG with the short stack in the BB will limp to induce a shove. Just be wary of that.

Calling isn't terrible given your stack size - meaning a call doesn't commit you to the pot . It's bad because your position sucks/ your villain's range is very wide and 66s are hard to play postflop. But you're basically getting a free look at the flop and if you don't like it, you can fold and move on.

Some opponents, with a big stack UTG with the short stack in the BB will limp to induce a shove. Just be wary of that.

This particular flop, I would lead out, shove a raise.

I agree that none of your options are terrible but as played I think you need to lead the pot and then call if he shoves. But I think I'd be happy with taking this pot down p/f with a shove as well!

You could lead...as I would probably do there...
or you could check and let him bet to try and pick up the pot...then raise all in. That may give him good odds to draw with over cards or like A10 or something.

Shove pre.

This is what I decided after. Not sure if he lays down the hand he had, probably not since it was A9ss. But a ton of those weak hands could lay down. I check raised him all in on the flop. I could have shoved the flop too. But, I agree, I should have shoved this pre.

Push PF. Very likely ahead, and you dont want to see a flop without the stack needed to set mine.