The other responder pointed out I was using the simplest terms, which frankly looks right to me. But the answer is more pedestrian. I read the information phrased it as 2/3 was diesel and 2/3 of the remaining amount was labor. So I eliminated the chain and simplified it to 2/3 and (1/3*2/3) 2/9.

I honestly didn't even notice the denominators were different. All of the fractions were in simplest terms, which is (imo) preferable to using a common denominator.