This law is called as Law of multiple proportions. It states that when two elements combine to give two or more compounds, then the masses of one element which combines with other is in ratio with one another.
For the 1st oxide , 57.2 parts of oxgyen by mass combine with 42.8 parts of carbon.
So, 1 part of oxygen combine with parts of carbon by mass= = 0.748
Similarly for the second oxide , 1 part of oxygen combines with parts of carbon by mass = = 0.374
So the ratio is 0.748 : 0.374 = 2:1 . Therefore it is a case of law of multiple proportions.