Bushing OK or need clamp? NM-B 6/3 going into breaker box
You'll need a 3/4" snap-in NM clamp that can be installed from the inside of the box

You do need a NM clamp (vs a mere bushing) here, first off; a simple bushing does not provide the clamping of the cable jacket required by NEC 312.5(C) for cabinets or 314.17(B)/(C) for boxes.  This NM clamp also needs to be installed from the inside of the cabinet, and that limits your options; in fact, the only product I know of offhand that fits the bill is the 3/4" Arlington NM95X, which maxes out precisely at 6/3.