Power supply gives 8 pin connectors exclusively for PCI Ex cards. if your PSU could support a card which requires 2 8 pin connectors it would have those connectors available. If your PSU has only one 6 pin and one 8pin (6+2) connector, i believe it cannot support a card which requires 2 8 pin connectors. I would recommend not using the card with some 6 pin to 8 pin adapter. The amount of power delivered will not be enough and that might cause issues.
Also i can't see that your PSU is 80+ certified. It might not even have a high efficiency which will make it even more risky to run the card. Please buy a new one, do not run the card with this PSU.