OK, so you'll need to try taking 3x+1 from two at a time.
6x^4 + 2x^3 = (2x^3)*(3x+1)
THEN
-6x^2 -2x = (-2x)*(3x+1)
THEN
-12x - 1 = (-4)*(3x+1)
So, you get (3x+1)*(2x^3-2x-4)
Cancel the 3x+1 from top and bottom and get:
2x^3 - 2x - 4
Hope that made sense!