If you don't have a raid then you should only need 3 4TB drives to achieve 12TB capacity. Most likely the Power supply can support that, but check the label on the PSU for the wattage and then you can use this calculator to confirm it is sufficient: eXtreme Power Supply Calculator
And as I said I THINK that the pcie sata controller would let you bypass the motherboard's limit on capacity but I haven't tried it so maybe someone else could chime in and confirm that.
Also if you're going that route you might want to get an additional smaller disk (maybe an SSD) to run just the OS, then you reserve the space on your 4TB drives
If you use windows 8 or 10 as your OS, you could use storage spaces to make a simple jbod array (no parity) with the 4TB disks.