I began this problem by considering which balls could occupy three boxes. I realized that only green and red could do so. It didn't seem like it would take that long to diagram these two options so I did.
For the diagram with green in three elements, I knew that any remaining Rs (of which there would be two, so that there would be R > W) would go in boxes five and six, leaving W in box one to complete the W/G chunk.
With Rs in 2, 3, and 4 I knew that I would still need to place the W/G chunk. The only remaining space for the chunk was slots 5/6. Heeding the second rule, I placed a G in slot one.
My two diagrams then looked like this:
6 R G
5 R W
4 G R
3 G R
2 G R
1 W G
The diagram with three green balls eliminated answer choice A. The diagram with three reds eliminated answer choice B. The diagram with three green balls eliminated answer choice C. D seemed fine when I considered it so I skipped down to E, which I got rid of with the first diagram.