Your computer system is utilizing a quad-core processor, which is capable of handling multi-tasking very well. I know some people don't really like the AMD Phenom processors, but I've used tons of them and they have been excellent performers!
Your system is 64-bit capable, so you can go ahead and throw as much RAM in there as you want. After all, it is the cheapest upgrade you can do to your computer and the easiest as well. RAM may make a difference to your overall performance if you have the need and can utilize it properly. What kind of software are you using specifically? As JFiscus mentioned above, are you using 32-bit or 64-bit versions of the Adobe products?
Design work, especially 3D design work or digital content creation and video production, can use all the RAM you can throw at it to help speed up the overall process, but in your day-to-day normal tasks having that large amount of RAM will make very little difference. My home computer here has 16 GB of RAM currently, and I have not once seen it go beyond using even half of that available RAM even when working in both Adobe Photoshop CS5 and Adobe Premiere CS5 together.
The pre-built system you have does have a dedicated graphics card, which is more powerful than integrated graphics that is standard in most pre-built desktop systems. However, it's a very entry-level card. If all you are doing is two-dimensional work then your graphics card really doesn't matter as much, most all of the work is done at the CPU. However, if you're working with 3D design you definitely need something more powerful for rendering and calculating those complex designs. Also, if you have newer versions of Adobe software, it can utilize your graphics card in some situations to greatly increase performance, such as applying renders or filter effects.
Here's the problem, though. The power supply in your pre-built desktop 99% of the time never supports more powerful graphics cards which can require additional power connections as well as higher output capabilities. To upgrade your graphics card, you'd need to upgrade your power supply as well most likely. I'd recommend this anyways as your power supply is the heart of your system and can make or break your entire computer if it fails.
The other option to upgrade your graphics card would be go to with a professional graphics card. This isn't a card designed for playing games, but specifically tailored for design work, content creation, and other professional industries. Many of them do not require additional power connections like gaming graphics cards, but are much more expensive than gaming cards. A good upgrade for you if you're doing 3D would be a PNY Quadro 600 which can be purchased for around $180. It's still rather entry-level if you're doing quite a bit of 3D work, but it's a noticeable step up from a GeForce 9400 GT graphics card.
