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No, Your Gigabyte Model has a FM2+ Socket while the A6-9500 requires a AM4 Socket.
Here are the detail specs on AMD A6-9500 APU: http://www.cpu-world.com/CPUs/Bulldozer/AMD-A6-Series%20A6-9500.html
Here are the Spec for your Motherboard from Gigabyte : GA-F2A68HM-DS2H (rev. 1.0) | Motherboard - GIGABYTE Global
Here are all the compatible FM2+ CPUs you can use on your Gigabyte Motherboard: