This tells us that 6 and 3 must be green, since many other color would violate the first two rules
_ G Y _ _ _ R G _ _
We also know that 1 must be red, since it cannot be yellow, and it also cannot be green
R G Y _ _ _ R G _ _
Finally, we know that since we've used up our yellows, the final two slots on the first row are one red and one green, although we don't know which order.