you motherboard specs are located at
http://www.gigabyte.com/products/product-page.aspx?pid=4669#sp
I see it can handle 2 x 1.5V DDR3 DIMM sockets supporting up to 16 GB of system memory, * Due to a Windows 32-bit operating system limitation, when more than 4 GB of physical memory is installed, the actual memory size displayed will be less than the size of the physical memory installed.
Dual channel memory architecture, Support for DDR3 1600/1333 MHz memory modules, Support for non-ECC memory modules, Support for Extreme Memory Profile (XMP) memory modules
your CPU though can only handle DDR3-1333 so getting DDR3-1600 memory would be wasting money as it will run at 1333 speed only.
http://ark.intel.com/products/77773/Intel-Pentium-Processor-G3220-3M-Cache-3_00-GHz
DDR3-1333 2x4GB to get a proper upgrade done, as your ram will have to be replaced due to only having 2 memory slots on your board
newegg sells them starting at 44$ : http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=100007611&IsNodeId=1&Description=DDR3-1333%202x4GB&bop=And&Order=PRICE&PageSize=36