Sata 3gb/s HDD on sata 6gb/s port

Solution
Yes, it'll work just fine. You're limited by the slowest component (so a 3GB/s HDD), although you don't actually max out the available speeds in 'normal' use.

You'll be fine.
Welcome to the community, Aron!

Just like @Barty mentioned, you shouldn't have any issues with the SATA II (3 Gb/s) HDD on a SATA III (6 Gb/s) port on the motherboard. Mechanical hard drives are not able to exceed the bandwidth provided by a SATA II (3 Gb/s) port, so a SATA III (6 Gb/s) would be even less likely to affect its performance.
Solid-state drives (SSDs), on the other hand, definitely NEED a SATA III port, because a SATA II one would definitely limit the transfer rate performance of the drive.
Here's a similar thread from the community that you might find interesting - SATA II vs SATA III HDD,

Hope this was helpful. Best of luck! :)
SuperSoph_WD