Yes having 6 Gb of total system memory can cause as you say stuttering in games.
Allow me to explain.
First of all every time you boot your pc and windows is loaded it sit`s, or takes up system memory as it is memory resident 100% all of the time during a windows session.
So in reality subtract what windows os takes out of the total of the 6Gb of physical memory you have.
That could leave you with around 4Gb of physical free storage space for other programs or games you wish to run.
When a game states it needs 8Gb of memory space it means 8Gb free space left after windows has loaded into memory if you are following this.
So it`s why if a game states it needs 8Gb of free system memory free. That you find most people to avoid lag spikes or a momentary freeze when playing a game or multiple annoying lag spikes opt to fit 16Gb of physical memory.
Having a system with a low amount of memory is not a good thing because windows will then resort to the swap filing
Or virtual page file used in windows and will severely cripple the performance of the system Alex.
Read up on what the page file of windows does.
http://lifehacker.com/5426041/understanding-the-windows-pagefile-and-why-you-shouldnt-disable-it
The windows Page file is about 100 times slower than the speed that physical memory can work at in speed on your system resulting in what you see due to the lack of enough physical free ram you have in Gb.
And the situation should be avoided at all costs by fitting more physical memory to as said 16Gb.
Lot`s of people fail to realize this, mainly because even for example you do have 8Gb of physical system memory fitted.
By the time windows has loaded into memory you don`t in fact have the total of 8Gb of free system memory the game states it requires to run optimally.