To find \( f(-4) \) for the function \( f(x) = \left( \frac{x}{8} \right)^2 \), we need to substitute \( -4 \) for \( x \):
\[ f(-4) = \left( \frac{-4}{8} \right)^2 \]
Now simplify \( \frac{-4}{8} \):
\[ \frac{-4}{8} = -\frac{1}{2} \]
Now we square this value:
\[ f(-4) = \left(-\frac{1}{2}\right)^2 = \frac{1}{4} \]
Thus, the value of \( f(-4) \) is
\[ f(-4) = \frac{1}{4} \]