To find \( f(-8) \) using the given function rule \( f(x) = -\frac{7}{x} - 12 \), we need to substitute \(-8\) for \(x\):
\[ f(-8) = -\frac{7}{-8} - 12 \]
Calculating the first part:
\[ -\frac{7}{-8} = \frac{7}{8} \]
Now substituting this back into the function:
\[ f(-8) = \frac{7}{8} - 12 \]
Now, to combine these values we need a common denominator. The denominator here is \(8\):
\[ 12 = \frac{12 \times 8}{8} = \frac{96}{8} \]
Now we can subtract:
\[ f(-8) = \frac{7}{8} - \frac{96}{8} = \frac{7 - 96}{8} = \frac{-89}{8} \]
Thus, the final answer is:
\[ f(-8) = -\frac{89}{8} \]