To find \( f(4) \), we start by substituting \( a = 4 \) into the function \( f(a) = -6(a + 1) - 7 \).
\[ f(4) = -6(4 + 1) - 7 \]
First, calculate \( 4 + 1 \):
\[ 4 + 1 = 5 \]
Now substitute this back into the function:
\[ f(4) = -6(5) - 7 \]
Next, calculate \( -6(5) \):
\[ -6(5) = -30 \]
Now substitute back into the equation:
\[ f(4) = -30 - 7 \]
Finally, subtract \( 7 \) from \( -30 \):
\[ f(4) = -37 \]
Thus, the simplified answer is:
\[ \boxed{-37} \]