Solve. \[ x^{4}-20 x^{2}+64=0 \]

Step 1 ：Let's rewrite the equation $x^{4}-20 x^{2}+64=0$ as a quadratic equation. We can do this by substituting $x^2$ with a new variable, say $y$. So, the equation becomes $y^2 - 20y + 64 = 0$.

Step 2 ：Solving this quadratic equation for $y$, we get the solutions $y = 4$ and $y = 16$.

Step 3 ：Substituting $y$ back with $x^2$, we get $x^2 = 4$ and $x^2 = 16$.

Step 4 ：Solving these equations for $x$, we get the solutions $x = -2, 2$ for $x^2 = 4$ and $x = -4, 4$ for $x^2 = 16$.

Step 5 ：So, the solutions to the original equation $x^{4}-20 x^{2}+64=0$ are \(\boxed{-2, 2, -4, 4}\).