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Will the 6/3 Romex be sufficient enough for the continuous draw of 48 amps for the home charger?

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Yup, I think you're correct. It’s been almost two years and probably why I drew single wires.
“6/3” is a designation for “6 gauge wires, three separate conductors” in a bundle.

Technically if using Romex you’d only need 6/2, as the wall connector doesn’t use the third conductor (neutral). Just two hots and a ground.