That cable you are showing allows you to power the case fan off the PSU (using the big 4-pin molex connector as you are doing) OR to power them off the motherboard using either the small 3pin male of female connector. They do this for maximum flexability depending on what the user has spare in their system and what motherboard they have etc.
You only need to plug in ONE OR THE OTHER NOT BOTH!
Powering a case fan directly from the PSU, as you are doing, usually allows you less ability to control rpm. Powering it off motherboard allows you sometimes to alter the rpm in the BIOS.
You can also buy, as others have mentioned above, a small adapter lead which once connected between the fan and however its being powered can automatically adjust the voltage down to 9v, 7v 5v etc from its 12v default depending on which one you buy. Less voltage means less rpm on the fan and so less noise, but of course it will be expressing less air volume as a consequence.
Or you can buy one which has like a knob on a pci bracket you fit and then you can turn up or down the fan speed outside the case depending on the pc's use. Finally the best and most expensive way is to buy a proper fan controller which fits into the front of your case and where you can control case fans fully.
I just plugged the fan directly into SYS_FAN1 on the mobo. In the BIOS, I see the RPM of the fan, but it doesn't let me edit it... So I download SpeedFan. I lower the percentage on Speed01 and the fan is still going full blast. I've tried Speed02 and Speed03 also. None of the numbers above change.
You can only control the speed of three fans. Looks like you have the high speed fan plugged in "Back Out" which would be Fan4. Plug that high speed fan into a different motherboard connection. Keep trying until you have it plugged into Fan1, Fan2, or Fan3.