A #6 AWG copper wire with 60 degree Celsius insulation rating can carry 55 amps, 75 degree Celsius insulation rating can carry 65 amps, and a 90 degree Celsius insulation rating can carry 75 amps. If it is aluminum or copper-clad aluminum the ampacity for the three temperature ratings would be 40, 50, and 60 respectively.
1 amp maximum.
The amount of current a wire can safely carry depends on the length of the run and the gauge of the wire, not just the wire size.
20 gauge copper wire can carry 1.46 amps. Insulated copper wire can carry 6.5 amps. This is assuming a short run of 25' or less.
The amps that a four gauge wire will handle will depend with the thickness of the wire. If the wire is thin, the four gauge will handle 95 amps.
AWG # 6 copper wire will carry 55 amps for service entrance wiring.