Let us define a function on the circle: Start at any point, the value is the gasolin left in the car. (Negetive value allowed.) After each point, the value is increased by the amount of gasolin at that point. This function reaches its minimum at some point. That point is the starting point.
This function is 0 at its start point, (at 0+, it is the amount stored at the point - Our function is right continuous ) and it is back to 0 when it comes back to the same point. If we change the start point, the new function is the same shape but differs by a constant, so the new start point is 0. If we choose the minimum point to be our start point, the function is always non-negative. So we can have enough gas to come back.