This study presents a comprehensive approach to calculating the free energy of hydration of methane using Molecular Dynamics simulations. We employed the Free Energy Perturbation (FEP) method to determine the Gibbs free energy associated with transferring a methane molecule into water. Simulations were conducted in a cubic simulation box containing one methane molecule and 1000 TIP4P water molecules. The forward and backward routes were both analyzed, providing consistent free energy differences, which validates the robustness of our methodology. The Gibbs free energy profiles demonstrated characteristic energy barriers and stabilization points, indicative of the interaction dynamics in the solvation process. The results demonstrate the robustness of the FEP method implemented in LAMMPS, yielding free energy in close agreement with experimental data and previous computational studies. The calculated free energy differences for methane hydration exhibited deviations of 13% and 8% for the forward and backward routes, respectively, compared to experimental values. These findings underscore the accuracy and efficiency of using LAMMPS for free energy calculations, contributing to the broader understanding of solvation thermodynamics. Additionally, radial distribution functions were analyzed to provide insights into the structural arrangement of water molecules around methane, revealing strong interaction between methane's carbon atom and water molecules.