6 flats? Find each hole, then look at the same location on the tire and rim. The problem will be there. (And if you are careful about not twisting the innertube when you put it in, you will know whether it is tire or rim.) I trust you always mount your tire with the label in the same place relative to the rim or some other way of relating tire and rim/valve. Label at the valve on the drive-side is the current "standard". Take your patched tube, place it against the wheel and look at the patch location for the problem. (I'll confess I have to look at both sides of the wheel, ahead and behind the valve, since I don't track which way I put inner tubes in.)
I've had many flats caused by the tiny wire from car/truck tire steel belts. Barely thicker than a hair and can be of length shorter than your tread and casing so as not to show either from the inside or outside. Those patches are a huge help in finding those wires. Until you fish it out, that wire will keep causing flats. Also inspect the rim strip and rim very carefully at the flat location.
Ben