High-order Raman scattering is a typical photophysical process in understanding the electron--phonon coupling (EPC) in materials. In a ``soft'' polar lattice, due to the strong EPC, the excited electron-hole pairs can be captured by the lattice deformation potential, forming the self-trapped exciton (STE). Although high-order Raman scattering mediated by STE has been predicted by theory, there are rare experimental reports, especially in the double perovskite ${\mathrm{Cs}}_{2}{\mathrm{Ag}}_{0.4}{\mathrm{Na}}_{0.6}{\mathrm{InCl}}_{6}$, with highly efficient white light emission. We observed high-order Raman mode up to 12 orders at 4 K in ${\mathrm{Cs}}_{2}{\mathrm{Ag}}_{0.4}{\mathrm{Na}}_{0.6}{\mathrm{InCl}}_{6}$ by resonance excitation. We propose a physical picture of high-order Raman scattering mediated by STE to explain well the linear dependence of frequency and linewidth with order number. A reduction in the EPC with a temperature increase is attributed to the breakdown of momentum conservation during high-order scattering and the delocalization of the STE. Our work deepens the understanding of the EPC in STE and inspires the research of the excited-state decay process.