Efficient catalyst design has garnered significant interest in recent decades due to its potential to address both the challenges of the greenhouse effect and energy shortages by facilitating the conversion of CO2 into valuable chemicals through catalytic reactions. To investigate maximizing the synergistic effects of supported PdAu catalysts, we conducted first-principles calculations on the activation and decomposition of CO2 and H2 on the PdAu/In2O3(110) system. The results demonstrate that the incorporation of a secondary metal (Au) into the supported Pd catalyst, in conjunction with precise control over Au concentration, exerts influence on both reactant binding energy and activation. The adsorption and activation of CO2 at the interface sites of Au4/In2O3(110) and PdAu3/In2O3(110) are not observed. The transition state for the dissociation of CO2 into *CO and *O is determined based on adsorbed CO2, providing insights into the properties of activated CO2. The Bronsted–Evans–Polanyi relation, which correlates activation barriers (Ea) with reaction energies (Er), was established for the CO2 dissociation mechanism on PdAu/In2O3(110) catalysts using equation E = 0.4Ea + 0.63. It was carried out to investigate the H2-dissociated adsorption processes and mobility energy on various PdAu/In2O3(110) catalysts. Finally, a highly efficient Pd2Au2/In2O3 catalyst for the hydrogenation of CO2 into methanol has been proposed. This research provides valuable insights into the hydrogenation of CO2 to methanol using bimetal-oxide catalysts and contributes to the optimization of the design of PdAu/In2O3 catalysts for CO2 reactions.