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Even if you were against only one opponent with top set it would be correct to call. You have 12 nut outs twice. I don't believe I would fold this hand on the flop no matter what the action.

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This would be a big mistake, especially heads-up. With the OP's hand, heads up he would have been a 65/35 dog. If the Villian had something like KKQJds instead of KKQ6ds, the OP would have scooped less than 15% of the time heads up.

The OP's flop play was fine. Had he seen the hands face-up, a call would have been appropriate, but there is nothing wrong with the lay-down here.