In the regime of stronger light-matter coupling, the fully quantum-mechanical results exhibit a more intricate rate profile. For instance, the major resonant peak, in addition to its heightened intensity and further broadening, is flanked by a side peak in the low-frequency regime around ω c = 600cm -1 . This secondary peak corresponds to a multi-photon process where the successive emission/absorption of photons in the cavity mode couples with the vibrational excitation/relaxation. The peak value varies, being higher or lower than one, depending on η c . Additionally, increasing the light- matter coupling strength η c results in a slight shift of the main peak. For instance, this peak reaches its maximum at ω c = 1185cm -1 for η c = 0.00125 a.u. , and it shifts to ω c = 1164cm -1 for η c = 0.01 a.u. This shift is due to the broadening effects of the molecular vibrational and cavity photonic states owning to their coupling to the baths. The photon with the cavity frequency lying between two vibrational transitional frequencies (1140cm -1 and 1238cm -1 ) can induce either the vibrational transition |v mol 0 + ⟩ → |v mol 1 -⟩ or |v mol 0 -⟩ → |v mol 1 + ⟩. The location of the peak maximum varies slightly upon changes in the molecule-solvent coupling strength, cavity-loss strength, and light-matter coupling strength. Conversely, the mixed quantum-classical results lack the peak features and instead predict rate enhancement inside the cavity across the whole frequency regime. Moreover, rates increase significantly in the high-frequency ω c regime, which is attributed to the larger The blue solid lines represent the converged results obtained from the fully quantum-mechanical approach with N cav v = 10. The blue dotted lines are the fully quantum-mechanical results with only the lowest photonic state involved in the simulations, i.e., N cav v = 1. The orange dotted lines correspond to the mixed quantum-classical treatment described in Sec. II, obtained by averaging over 1000 trajectories.