Can this this run a gigabyte 6850 0c

DM186

Splendid
To me that is a generic PSU and would not trust it at all even if it has the right amount of amps on the 12v rail you could later on have it fail and you could be out of a PC and everything in it.

The 6850 OC'd will use more tha 117w and since you have only one rail and it is 17amps. It would run that card but we are not looking also how much your CPU and other hardwear is using.

Bottom line is it will run the card. But for how long and what will it do to your rig if something should go wrong. Look for brands like Corsair, Antec, Seasonic, and XFX PSU's.

A good 500w should do the trick I have added two links to newegg. I do wish you the best on this and good luck.

http://forums.overclockers.com.au/showthread.php?t=532741

http://forums.whirlpool.net.au/archive/855479

http://www.newegg.com/Product/Product.aspx?Item=N82E16817371035

http://www.newegg.com/Product/Product.aspx?Item=N82E16817139027
 
I wouldn't run a card like that on a PSU such as that.
Reviews show that PSU isn't good at all.
http://****/wp/2011/12/31/the-el-cheapo-power-supply-round-up-2/4/

Get a Corsair CX 430W PSU or so. It's really a good one and can handle a HD 6850 or HD 6870.