The number of cores isn't that important. The architecture of the FX-6300 is much better and efficient than the 8120's architecture, the 6300 also has a higher clock speed and, combined with the better, newer architecture, has much better single-threaded performance. This is very important in games because games have only just started to use more than 2 cores, most games are far from using 6, let alone 8. Therefore, 2 strong cores vs 2 weak cores in the average game, the 6300 wins there.
Until you get into the 8th core of the 8120, the 6300 will be more powerful. Therefore, the 8120 has to use all 8 cores to perform slightly better in multi-core performance which isn't really good in a gaming build, like I stated before.