The rule implies that C must always sit behind B, and B must always be behind A. This placement constraint leaves their order as A, B and C. So, they can be thought of as a single unit. Now, including D, E, and F, we have a total of 4 units to be seated. These can be arranged in 4! ways which equals 24. Within the ABC unit, A, B, and C can shuffle between themselves in 3! ways which equals 6. By the multiplication principle, the total ways equals 24*6=144.

The options provided are 60, 72, 120, and None of the Above. But none of the options match the calculated 144 ways.

Alert - correct answer should be "None of the Above". The numerical answer being 144 is absent in the list.