= Solution
<Neutrino decoupling> occurs when the interaction time ceases to be short compared with the expansion time, or $\Gamma\simeq H$. In <natural units>, this gives
$$
G_\nu^2T_{\rm dec}^5=1.66\frac{\sqrt{g_*}\,T_{\rm dec}^2}{M_{\rm Pl}},\qquad T_{\rm dec}=\left(\frac{1.66\sqrt{g_*}}{G_\nu^2M_{\rm Pl}}\right)^{1/3}.
$$
Using the supplied high-temperature estimate $g_*\simeq100$,
$$
\boxed{T_{\rm dec}\simeq\left(\frac{16.6}{10^{-24}\times1.2\times10^{19}}\right)^{1/3}\!\mathrm{GeV}\simeq1.1\times10^2\,\mathrm{GeV}.}
$$
Here $M_{\rm Pl}$ is the unreduced <Planck mass>. The scaling $\Gamma/H\propto T^3$ explains the direction of the transition: interactions maintain <thermal equilibrium> at high temperature, but become ineffective as the universe cools. The extra species changes $g_*$ only by a small amount compared with the precision of the estimate.
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