\(\left(a-2\right)^2=16\)
\(\Leftrightarrow\left(a-2\right)^2=\pm\sqrt{16}\)
\(\Leftrightarrow\left(a-2\right)=\pm4\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}a-2=4\\a-2=-4\end{array}\right.\Leftrightarrow\left[\begin{array}{nghiempt}a=6\\a=-2\end{array}\right.\)
Vậy \(a\in\left\{6;-2\right\}\)