Unfortunately, the problem is not with your system memory, but with your graphics memory.
This generation of video card is, at best, 6 years old and simply does not have the necessary memory to store all of the required textures. I'd look for an inexpensive video card to upgrade to which should not only allow you to play the game, but should give you a nice performance boost in the process.
Also to note, the version of OpenGL supported by this card will not even be sufficient to run vanilla Minecraft in the future, so an upgrade will be needed sooner or later. https://help.mojang.com/customer/portal/articles/1307761-future-opengl-support
It's got NOTHING to do with his gfx card, please don't talk nonsense...
You need more RAM, if you checked the Direwolf20 thread you would see countless people with this issue. 4Gb installed is NOT enough.
Use the damn thread plse: http://forum.feed-the-beast.com/threads/direwolf20-1-7-10-help-venting-and-discussion-thread.54927/