Hi,
I think the calculation is correct, but it does not include the efficiency of the inverter. That is, when the inverter is putting out 2300 watts on its output side, and if its 90% efficient, then its input wattage will be (2300 watts) / (0.9 efic) = 2555 watts, and your calc for amperage would be (2555 watts) / (12 volts) = 213 amps.
Wire sizing is a 2 step deal. The current in the wire cannot exceed the ampacity rating for the wire and the voltage drop along the wire should not exceed about 2%. The table you are using only accounts for voltage drop. The 213 amps would exceed the ampacity rating of
#6 wire by quite a bit, and I would not use it -- the wire is likely to overheat.
BlueSea has a calculator you can use that accounts for both ampacity of the wire and voltage drop.
http://circuitwizard.bluesea.com/
So, if you go into the calculator with 12 volts, 213 amps, insulation rated for 90C (most common), total length of conductor 2+2 = 4 ft, and 2% for voltage drop, the calculator comes up with AWG 0.
This is what I'd use.
I'd also take careful look at the user manual for the inverter. In my experience, they usually want a wire that is even larger than what the calculator gives. If it does recommend a larger wire, I'd go with that.
You will want a fuse or breaker near the battery end of this wire.
edit: Not to beat this to death, but when you run the calculator at the link above, after you press Calculate then click the button that says "Explain Results". As it explains, the wire gage for ampacity (maxium allowed current for a wire) is AWG 0, while the acceptable wire gage for voltage drop is AWG6. So, AWG 0 is required to keep the wire from overheating even though AWG 6 would be OK for voltage drop.
On another page on the BlueSea site, they say that currents in excess of the 150% of the maximum ampacity that the insulation will melt off the wire. AWG 6 has a maximum ampacity of about 100 amps, so at 230 amps you will be well over the current at which the insulation will melt.
I promise -- no more edits
OK, one more. You mention using a 250 amp fuse on a #6 wire -- this is just way to large breaker or fuse to use on a #6 wire -- it may provide some protection to the wire in the case of a hard short to ground, but provides essentially no protection for overloads.
Gary