That should work fine, although generally graphics cards are shipped with one of those converters in the box.
In short the 4 pin molex and the 6 pin PCIe connectors do the same thing, supply power, but the 6 pin handles larger wattages, thus the converter needs 2 4 pin molexes to convert enough power into a 6 pin.
It is hard to tell from your picture but theres a chance there is a 6 pin connector between those tangled wires coming from the psu (the black / red / yellow bunch). If there is not, just plug 2 4 pin molexes from the PSU into the converter, and the 6 pin end into the card.
If the PSU doesnt have a 6 pin, and doesnt have 2 4 pin molexes you are out of luck as the PSU would be incompatible with the card.
You will probably have to cut the black plastic strap holding the wires together, you can tidy these together again once your system is up and running.
edit: unfortunately I made a typo while editing the pic, the bottom one I noted is a 4 pin molex.