Do you have a meter on the DC side to show how much voltage and current was going in?
What breaker tripped?
What is it's rating? I can't read the number in the picture.
Was the breaker current rating close to the current draw?
Could be a bad breaker. Or even miss labeled. I ordered a 150 amp breaker like that, and they sent me a 40 amp unit. The package had a sticker on it that said 150 amps. Under the sticker it has a label that said 40. I returned it and they sent another 40. I complained and they sent me yet another for free, it was also a 40. REALLY!! I still have the two here, it was not worth trying to return it again. Try replacing the breaker with a 200 amp Class T fuse.
Those inverters are not the best quality, but they should be able to deal with about half rated power without a problem. But on just 24 volts, 6,000 watts is 250 amps. That is a ton of current. Even your 1,600 watt load could be looking for over 70 amps when you figure in inverter efficiency and other losses. My inverter is rated at 6,800 watts, but I am on a 48 volt system, fused at 200 amps. I have run to up to about 4,000 watts in testing with no issues, but it is a Schneider inverter that costs $3,000 US. And all my wiring is well sized an using quality Bussman and LittleFuse brand fuses on Blue Sea fuse holders.