In a compost pile, food and dry leaves are broken down into simpler substances by bacteria and fungi. what carbon cycle process is at work?

ammonification
decomposition
photosynthesis
respiration

 Decomposition

Decomposition is a process, during which microbes like bacteria and fungi gets colonize over the dead remains of plants and animals. A compost pile is created when the partially degraded material obtain from plant and animals gets mixed with the components of soil. The compost pile allows the colonization of microbes. These microbes convert the contents of the compost pile into simpler substances or elemental forms. The organic matter present in the compost pile is a rich source of carbon. The decomposers feed on the nutrients present in the compost pile. They release carbon to the soil and the atmosphere in the form of carbon dioxide by the process of respiration.  

Therefore, in the given condition, the carbon cycle process is at work is decomposition.

1 and 6 for apex