How many watts can run through 12-3 wire?

Wire is rated in ampacity, You can use only 80% of the rated ampacity. Voltage and amperage are inversely proportional. So at 120 volts alternating current you safely run 1800 watts ( I have added a small safety margin). At 240 volts you can run 3600 watts.

I hope this has answered you question

Ampsxvolts=watts watts/volts=amps