12 AWG. You can run several hundred feet.
3/0 gauge
Use 8 gauge wire.
AWG #6
2 AWG.
At the service entrance you will need AWG 1/0 gauge.
3/0 gauge
Use 8 gauge wire.
Someone would need to know what gauge the wire is to answer that.
Wire gauge is used to determine the size wire needed to carry the correct amount of current for the job. It must be sized appropriately for the current in the circuit you are building.
4 gauge
The guage of wire for 20 amps is #12 copper.
AWG #6
2 AWG.
10 AWG.
At the service entrance you will need AWG 1/0 gauge.
A 100 foot fish tape and wire lubrication will be needed to make this wire pull.
As a service entrance wire you need AWG # 3/0 gauge copper.