I have the Brother CS6000i ----DO NOT OIL ---
E6 means there is a thread problem- usually in the bobbin area - have you done all the normal steps- rethread top of the machine - new needle- new bobbin in the bottom ? I use a qtip to clean out under my feed dogs after taking the bobbin out -- check the bobbin to make sure the thread is coming off the bobbin correctly when it comes off the bobbin it should be over the center of the bobbin -- and for some reason with this machine the thread spool feeds off from the front not the back :wink: Does that make sense ?
Good Luck