In a cyclic process, system returns to its initial state.
If an amount of heat Q is given to a system a part of it will be used in increasing the internal energy (ΔU) of the system and the rest is doing work (W) by the system.
Therefore, Q=ΔU+W (first law of thermodynamics)
The internal energy of the system does not change in a cyclic process (ΔU=0) because it is a function of only the state of the system. ∴Q=W
Hence, in a cyclic process, the heat given to a system equal the net work done by the system.