What can a AMD FX-8320 run?

The question does not make a lot of sense. Gaming is mostly about the graphics processor. An insufficient CPU can cause performance issues when the graphics is sufficient for settings of a game.
An FX-8320 can be overclocked into an FX-8350 or higher performance with a good cpu cooler.
However also, Crysis-3 can use all 8 cores, and there's discussion that BF4 uses more than 4 cores when available, but otherwise, an FX-8xxx is not much better than an FX-4xxx in gaming if not multi-tasking. The FX-x3xx are all physically the same CPU. AMD locks or unlocks cores and sets the clock and tests it. Also, FX-8xxx is not a true 8 core, because an AMD core and Intel core are not defined the same way. AMD has some resources of the CPU shared.

Add in the graphics card and there may be test results or estimations available. Guessing gaming performance of the fx series is a game unto itself.

There's disagreement, and performance is an average of many games, but here is a hierarchy
http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106-5.html

With a gtx-660 - Minecraft should max out to the display capability.
COD Ghosts - High settings in the 40's fps on 1080p, and pushing ultra
http://www.game-debate.com/...quirements
http://www.notebookcheck.net/...849.0.html

bf4 ultra in the low 30's fps on 1080p
http://www.game-debate.com/...quirements

Any dual/quad /6/8 core processor can run the games mention what we need to know the graphic card that going with the amd fx 8320

I agree with what Starpc said, we need to know what GPU you are getting.

The CPU will be fine, but you're leaving out the GPU, which is an important question with gaming.

We need to know the GPU you have or you are getting. I have an AMD FX 8320, it's pretty good, but I have an R7 260x graphics card. That equals out to be something like a GTX 650ti. I run Minecraft singleplayer at 120 FPS at all times. Shaders is very demanding though, I get around 20+ FPS in singleplayer. Multiplayer is a different story. Above 60FPS at all times unless in a lobby with a ton of people. (Without Optifine or shaders) BF4 should run at High at 30+ FPS at 1080p. COD Ghosts, High settings at 30+ FPS most likely. Sniper Elite v2 Ultra (Without Extreme Shading) at 1080p, EASILY 60 FPS.