If hubby says a 6 year old child is big enough to stay at home by himself anyway he knows what to do, is he correct or wrong?

6 years old, still too young. You can do some mini tests and observe. E.g. ovserve what he would do when a stranger knocks on the door (does he call another adult to check or tries to open the door), what happens when he is thirsty and you're too busy to pour him water (does he know how to get himself a cup/glass of cold/hot water) etc.... observing his little responses and behaviour would let you know if he is ready to be left alone.