You cannot run DVI-A and VGA at the same time on the HD 6670, since it only has one RAMDAC, unfortunately, you will have to buy an Active DVI-D or HDMI to VGA converter, or you just find a screen that supports DVI-D.
DVI-A stands for DVI-Analogue, it is a backward compatible signal that is the same as VGA, so it is basically VGA signal, but on a DVI connector.
DVI-D stands for DVI-Digital, it is pure digital signal on the DVI connector.
A Passive converter is just basically a cable that puts the pins differently where it "should work".
An Active converter is really converting the signal, but they cost much more $.
Be sure that it is DVI-D, not A.
Hope it helps!,
-Bloc97