6144MB RAM
alright, now that we know you have enough ram to spare.
1. go into your sims game folder. not the my documents folder but the actual game folder. Find a file called sims3.ini
2. open the file and look for "memoryusagelimit ="
As you can see, I changed mine to use 10 GB of ram. Those extra zeros are necessary. So for you, since you only have 6 gb, put it to 40000000 instead because you need 2 extra gbs for your computer. if you put it any higher, you'll run into some issues. 4 gb is plenty for the sims.
save the file and exit. now launch the sims and tell me if its running any better.