The mass of carbon in a sample can be determined by measuring the mass of the sample and then subtracting the mass of any other elements present in the sample. For example, if you have a sample that contains both carbon and hydrogen, you could determine the mass of carbon in the sample by measuring the mass of the sample, then measuring the mass of the hydrogen present in the sample, and subtracting the mass of the hydrogen from the mass of the sample.
Alternatively, the mass of carbon in a sample can be determined by analyzing the sample using a technique such as elemental analysis or mass spectrometry. These techniques allow you to determine the relative amounts of different elements present in a sample, including carbon.
In the case you provided, it is not clear how the mass of carbon in the sample was determined. It is possible that the mass of the sample and the mass of any other elements present in the sample were measured and used to calculate the mass of carbon, or that the sample was analyzed using a technique such as elemental analysis or mass spectrometry.