To find \( f(-3) \) for the function \( f(x) = \left(\frac{x}{12}\right)^2 \), we substitute \( -3 \) for \( x \):
\[ f(-3) = \left(\frac{-3}{12}\right)^2 \]
Simplifying the fraction inside the parentheses:
\[ \frac{-3}{12} = -\frac{1}{4} \]
Now, we square this value:
\[ f(-3) = \left(-\frac{1}{4}\right)^2 = \frac{1}{16} \]
Thus, the value of \( f(-3) \) is
\[ \boxed{\frac{1}{16}} \]