The distance traveled by an object can be calculated by multiplying the average velocity by the time of motion. In this case, for option II, the average velocity is +3.0 m/s and the time of motion is 2.0 s, resulting in a positive distance traveled. For option I, the average velocity is -4.0 m/s and the time of motion is 2.0 s, resulting in a negative distance traveled. For option III, the average velocity is -3.0 m/s and the time of motion is 3.0 s, resulting in a negative distance traveled. Therefore, the correct order of distances traveled in increasing order is II, I, III.