Functions $f$ and $g$ are defined on the set of real numbers as
$$\begin{aligned}
& f(x) = \frac{3x + 4}{2} \\
& g(x) = \frac{2x - 4}{3}
\end{aligned}$$
If $(\mathbf{f} \circ \mathbf{g})(\mathbf{a}) = \mathbf{f}(\mathbf{a}) = \mathbf{b}$, what is the product $\mathbf{a} \cdot \mathbf{b}$?
A) $-20$
B) $-12$
C) $-8$
D) 4
E) 16