To find \( f(-4) \) for the function \( f(x) = 4x^2 - 4 \), we will substitute \(-4\) for \( x \) in the function.
\[ f(-4) = 4(-4)^2 - 4 \]
Now, calculate \((-4)^2\):
\[ (-4)^2 = 16 \]
Now substitute that back into the equation:
\[ f(-4) = 4 \times 16 - 4 \]
Now calculate \(4 \times 16\):
\[ 4 \times 16 = 64 \]
Now substitute that into the equation:
\[ f(-4) = 64 - 4 \]
Finally, calculate \(64 - 4\):
\[ 64 - 4 = 60 \]
Thus,
\[ f(-4) = 60 \]
So, the final answer is:
\[ \boxed{60} \]