Im getting a bit lost here.
Your case has 2 usb 3 ports ?? They should be coloured blue?.
The 20 pin cable you pictured should already be built into the case , it,should also be linked to both usb 3 ports , that single cable is made to run 2 x usb 3 ports.
I have NEVER seen.
1. A case with usb 3 that doesnt come with the header cable already attached or supplied
2. A pair of usb 3 ports requiring more than a single cable/ board header.
You need to clarify what you actually need ?
In the same position I use this exact card with an old amd 760g board like yours & a newer case with usb 3 ports.
It has a single 20 pin usb header to fit that cable you pictured & also a 4 pin molex because these adapters need external power from the psu.
CSL USB 3.0 PCI express (PCIe) controller | 2 x external (ports) / 1 x internal (controller/header) | USB 3.0 Super Speed interface card | USB internal hub
https://www.amazon.co.uk/dp/B00VE6KHB6/ref=cm_sw_r_cp_apa_pZjUBbA2MW74E