Graphic cards has something call a RAMDAC (Random Access Memory Digital-to-Analog Converter) while allows only two signals to be from the GPU chip to the monitors. Graphic cards generally only have one RAMDAC. So regardless if the card itself has 2 VGA ports, 2 DVI ports and 2 HDMI ports, only 2 of those 6 ports can be used at any one time.
Cards with DisplayPort (AMD EyeFinity / nVidia 3D Surround) can be connected to 3 or even 4 monitors. DisplayPort has it's own RAMDAC which is why 3 monitors can be connected. If the RAMDAC for the DisplayPort is also connected to a VGA, DVI, HDMI or another DisplayPort, then potentially 4 monitors can be connected.
Since your card only has one RAMDAC the easiest and likely cheapest solution is to...