Can I overclock my FX 8320 on my Gigabyte M68MT-S2?

Hi and welcome to Tom´s forum.

You can overclock with that motherboard but I will really suggest you don't do it. The model that you have is designed for basic use and not for overclock, can handle just basic things and PWM regulation isn't the best.
 
970 or 990 motherboard should work
I have this motherboad and was able to overclock my 8350 to 4.5
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131873&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-_-na-_-na-_-na&cm_sp=&AID=10446076&PID=3938566&SID=
This is also a great motherboard
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131874&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-_-na-_-na-_-na&cm_sp=&AID=10446076&PID=3938566&SID=
You can also cf/sli with it.