Let $\mathbb { R }$ denote the set of all real numbers. Let $a _ { i } , b _ { i } \in \mathbb { R }$ for $i \in \{ 1,2,3 \}$.

Define the functions $f : \mathbb { R } \rightarrow \mathbb { R } , g : \mathbb { R } \rightarrow \mathbb { R }$, and $h : \mathbb { R } \rightarrow \mathbb { R }$ by

$$\begin{aligned}
& f ( x ) = a _ { 1 } + 10 x + a _ { 2 } x ^ { 2 } + a _ { 3 } x ^ { 3 } + x ^ { 4 } \\
& g ( x ) = b _ { 1 } + 3 x + b _ { 2 } x ^ { 2 } + b _ { 3 } x ^ { 3 } + x ^ { 4 } \\
& h ( x ) = f ( x + 1 ) - g ( x + 2 )
\end{aligned}$$

If $f ( x ) \neq g ( x )$ for every $x \in \mathbb { R }$, then the coefficient of $x ^ { 3 }$ in $h ( x )$ is

\begin{center}
\begin{tabular}{|l|l|}
\hline
(A) & 8 \\
\hline
(B) & 2 \\
\hline
(C) & -4 \\
\hline
(D) & -6 \\
\hline
\end{tabular}
\end{center}