This study explores the potential of cubic ternary hydrides X₂MH₆ (where X = Li, Na, Mg, Al, K, Ca, Ga, Rb, Sr, and In; M = 3d, 4d, and 5d transition metals) as high-temperature superconductors (high-$T_c$) at ambient pressure. The researchers performed a high-throughput screening of these compounds based on their electron-phonon coupling strength (EPC) at the Γ point, which is a key descriptor for identifying conventional superconducting materials. Among the 290 candidates, 26 compounds were found to be dynamically stable and exhibit strong EPC. Further analysis revealed that six compounds, including Mg₂CoH₆, Mg₂RhH₆, Mg₂IrH₆, Ca₂PdH₆, Al₂MnH₆, and Li₂CuH₆, are thermodynamically stable with an energy above the convex hull (Ed) less than 80 meV/atom. Among these, Mg₂RhH₆, Mg₂IrH₆, Al₂MnH₆, and Li₂CuH₆ show promising superconducting properties with critical temperatures (Tc) exceeding 50 K. The electronic structures of these compounds, characterized by sharp van Hove singularities at the Fermi level, are discussed, and their EPC and Tc values are calculated. The study highlights the potential of these compounds as candidates for experimental synthesis, with Li₂CuH₆ showing a Tc of 80 K, surpassing the liquid nitrogen temperature. This work provides a significant contribution to the search for high-$T_c$ superconductors at ambient pressure.This study explores the potential of cubic ternary hydrides X₂MH₆ (where X = Li, Na, Mg, Al, K, Ca, Ga, Rb, Sr, and In; M = 3d, 4d, and 5d transition metals) as high-temperature superconductors (high-$T_c$) at ambient pressure. The researchers performed a high-throughput screening of these compounds based on their electron-phonon coupling strength (EPC) at the Γ point, which is a key descriptor for identifying conventional superconducting materials. Among the 290 candidates, 26 compounds were found to be dynamically stable and exhibit strong EPC. Further analysis revealed that six compounds, including Mg₂CoH₆, Mg₂RhH₆, Mg₂IrH₆, Ca₂PdH₆, Al₂MnH₆, and Li₂CuH₆, are thermodynamically stable with an energy above the convex hull (Ed) less than 80 meV/atom. Among these, Mg₂RhH₆, Mg₂IrH₆, Al₂MnH₆, and Li₂CuH₆ show promising superconducting properties with critical temperatures (Tc) exceeding 50 K. The electronic structures of these compounds, characterized by sharp van Hove singularities at the Fermi level, are discussed, and their EPC and Tc values are calculated. The study highlights the potential of these compounds as candidates for experimental synthesis, with Li₂CuH₆ showing a Tc of 80 K, surpassing the liquid nitrogen temperature. This work provides a significant contribution to the search for high-$T_c$ superconductors at ambient pressure.