I wanted to play my Mobile Suit Gundam: Zeonic Front game and no matter what I try the FPS go down to 20FPS. How can I speed this game up.

I have an Intel quad core processor at 2.4GHz
6 GB DDR2 ram
GeForce 9300 GE

You could try some speedhacks. I don't know how much that will help. You can also try overclocking your CPU. If you don't know what that is, then you probably shouldn't try it, or at the least, research about it before trying it. Other than that, you could also try the latest PCSX beta and the latest GSDX beta.

OC your CPU.
Use the latest public beta release and not the 0.9.6 version.
Use the latest GSdx revision.
Enable all speed hacks, set VU Cycle Stealing to Moderate.
In the GSdx configuration, use Dx10 hardware and Native Resolution.

Depending on your CPU I'd say your bottleneck is your lousy GeForce 9300 GE card, in which case an upgrade would deliver a higher FPS.