How do you check which cable size is suitable for 4 KW motor?

Cables are rated are by the max current they can supply. To work out the current load you need to divide the Watts by the Voltage (which is either 120 or 240 depending on where you are).

In the UK: 4kW/240V = 4000/240 = 16Amps, so the cable would probably be rated for 20 amps.

In the US the current is 32Amps, so the cable would probably be rated for 50 amps.