Answer
$t =1 \times 10^{-3} \,\text{s}$
Work Step by Step
For $x = -0.8 x_{m}$. the time $t$ will be
\begin{gather*}
x=x_{m} \cos (\omega t+\phi) \\
-0.8 x_{m}=x_{m} \cos ((165 \mathrm{rad/s} ) t + 0.64 \mathrm{rad} )\\
\cos ^{-1}(-0.8 ) = (165 \mathrm{rad/s} ) t + 0.64 \mathrm{rad} \\
t =1 \times 10^{-3} \,\text{s}
\end{gather*}
