Measure 208v single phase with Current Transformer

A 240 volt motor will only be connected to the two live wires, not to neutral, so your example draws 6.6 amps at 240 volts. If it is connected to operate at 120 volts, it will be connected between one live wire and neutral, and will draw 13.2 amps at 120 volts.

I think it is misleading to say that, in the 240 volt case, the motor draws 6.6 amps from each live wire. A more correct description would be that it draws 6.6 amps from one live wire, and returns that 6.6 amps through the other live wire.

Using the same terminology, in the 120 volt case, the motor will draw 13.2 amps from the live wire, and return that 13.2 amps through the neutral wire.

On any individual circuit (lamp or 120V outlet) the current in the neutral in that circuit is equal to the current in the "hot" wire.

If you have equal loads between black and neutral, and between red and neutral, the "black" current and the "red" current will cancel in the neutral - there will be no current in the shared neutral wire.

Anything that only uses 240V (hot water heater?) will not connect to the neutral, and therefore will not cause any neutral current.

An electric stove will use 240 V for the heating elements, but also uses some 120 V for lights and a clock, so will require a neutral connection, and so will generate some neutral current.

The current in the neutral wire between your house and the power company's transformer will depend on how the loads in your house are balanced between the two "hot" wires.