In the decays of $\eta_c\to\gamma\gamma$ and $J/\psi\to\gamma\eta_c$, there are discrepancies between the theoretical calculations and the PDG experimental values, referred to as the charmonium QCD puzzle. We observe the decay $\eta_c\to\gamma\gamma$ in $J/\psi\to\gamma\eta_c$ using $(2712.4\pm14.3)\times10^{6}$ $\psi(3686)$ events collected with the BESIII detector, and determine the product branching fraction $\mathcal{B}(J/\psi\to\gamma\eta_c)\times\mathcal{B}(\eta_c\to\gamma\gamma)=(5.23\pm0.26_{\rm{stat.}}\pm0.30_{\rm{syst.}})\times10^{-6}$. This measurement is consistent with the two most recent lattice QCD calculations, providing significant input toward resolving the charmonium QCD puzzle.