Hmm, My DS (10), has been a right sod for a couple of months. Never did anything when asked, threw tantrums when expected to do homework/tidy room/do his standard chores. Cheeky talk, showing little respect.
On Friday, over dinner, I said we had had enough. TV and Computer time were banned, and bedtime would come forward by an hour. This situation would stay in place until his behaviour settled down, and he realised that he should show us the consideration and care that we show him.
Friday evening he grumped and groaned. On saturday he was a bit grumpy in the morning, but settled to do his weekend homework with little disruption.
We had a much more settled sunday and monday, and by tuesday morning he got up and did one of his jobs (emptying the dishwasher) before we even got out of bed. He has even brought us early morning tea on 2 mornings !!!
By the second half of this week, we have a much calmer house, cos he's not yelling at us, so we don't have to shout at him (or each other). I have allowed some computer time tonight, and he can watch TV with me later.
DS and I are making sure to tell him how much we like this improvement, thank him profusely every time he responds well to a request.
I don't know whether it will last, but privileges such as PC & Telly time will be allowed only while bedhaviour is good. Oh and I have banned ALL crap american kids programmes for good.
Maybe your 6 y.o. needs pulling up short.