Let $a$, $b$, $c$, and $d$ be real numbers such that
$$\begin{aligned}
& a x ^ { 2 } + b x + 12 \geq 0 \\
& c x ^ { 2 } + d x + 24 \leq 0
\end{aligned}$$
To find the solution set of this system of inequalities, the following table is constructed and the solution set is found to be $[ - 2 , - 1 ] \cup [ 4,6 ]$.
What is the sum $a + b + c + d$?\\
A) 15\\
B) 16\\
C) 17\\
D) 18\\
E) 19