I'm no expert on inverters, so maybe temper that with something I'm not familiar with when it comes to inverters....but, an inverter that is capable of 2000 Watts is going to draw a lot of current on the DC side of things. 2000 watts output from the inverter is roughly 16 1/2 amps of 120 vac. In order to get that output, the input has to be able to supply roughly 2000 watts. With the input voltage being lets say 12.4 VDC, you would be pulling (2000 watts divided by 12.4 volts) around 160 amps on the DC side of the circuit. So absolutely NO, there is no way a 6 ga wire is going to do that.
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