The question asks us to relate the carbon cycle with one of the following laws: Law of multiple proportions, Law of definite composition, First and Second Law of Thermodynamics.
At first, let's recall what is the carbon cycle: in simple words, the carbon cycle is the flow of carbon between different reservouirs (water, earth, plants, atmosphere etc.), occuring an exchange of carbon and basically maintaining the carbon amounts on Earth.
Now, we can relate the carbon cycle with one of the laws proposed. From the options given, the First Law of Thermodynamics, which is very similar to the Law of Conservation of Energy ("the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed"), would be the one closer to what the Carbon Cycle means. Therefore, the best option would be the 4th one, the first law of thermodynamics.