Here is my take on it:
Suppose the truck starts out at point A and travels 216 miles to point B using 216/ 12 = 18 gallons of gasoline. At point B, the expedition deposits 54 gallons and returns to point A using up the remaining 18 gallons. This trip is repeated, so that another 54 gallons is deposited at point B. Point B, which is 216 miles from point A, now has deposits of 54+54 = 108 gallons of gasoline. The truck then starts out again from point A fully loaded travels to point B, and picks up the 18 gallons there which was used up to make the trip from point A to point B. Thus, there are 90 gallons now stored at point B. Then, fully loaded with gasoline, the truck proceeds to point C which is 576 miles from point A, but only 360 miles from point B. The truck then used up 360 / 12 = 30 gallons to get to point C. The expedition deposits 30 gallons at point C and returns to point B where the empty tanks of the truck are filled with 90 gallons from the gasoline stored there. Then, the truck proceeds again to point C, using 30 gallons, picks up 30 gallons there, and fills the tank again. At a full capacity of 90 gallons, the truck starts out from point C across the desert and travels the remaining 90×12 = 1080 miles to its destination. Thus, the expedition has used three full tanks of gasoline, or 90×3 = 270 gallons!!.
