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Theoretical investigation of hydrogenation processes has applied to magnesium diborides under ambient conditions, which identified two structurally stable phases, i.e, Mg4B6H2 4 B 6 H 2 and Mg4B4H4. 4 B 4 H 4 . These identifications were evaluated through assessments of their lattice dynamics stability using density functional perturbation theory. Both phases exhibit metallic behavior within their electronic band structures. Our findings showcase the significant impact of anisotropic Migdal-Eliashberg calculations, enhancing the superconducting properties within this system and resulting in a notably higher T c of 34 K. Mg4B4H4 4 B 4 H 4 exhibits superconductivity with a T c of 17 K under atmospheric conditions, as determined by anisotropic Migdal-Eliashberg calculations. Our study underscores the wide range of structural variations achievable through the hydrogenation of MgB2 2 and highlights the crucial importance of hydrogen atom placement within these structures. In addition, the calculation result indicates the influence of band dispersion characteristics on Fermi velocity, a factor attributed to both anharmonicity and harmonicity, which plays a pivotal role in determining the superconducting properties of these materials.