To find \( f(-4) \) for the function \( f(x) = \left(\frac{x}{8}\right)^2 \), we can substitute \(-4\) for \(x\):
\[ f(-4) = \left(\frac{-4}{8}\right)^2 \]
Now simplify the fraction:
\[ \frac{-4}{8} = -\frac{1}{2} \]
Next, square this result:
\[ f(-4) = \left(-\frac{1}{2}\right)^2 = \frac{1}{4} \]
Therefore,
\[ f(-4) = \frac{1}{4} \]
The answer is \( f(-4) = \frac{1}{4} \).