Use the transformation $u = 3x + 2y$, $v = x + 2y$ to evaluate the given integral for the region R bounded by the lines $y = \frac{3}{2}x + 1$, $y = -\frac{3}{2}x + 4$, $y = -\frac{1}{2}x$, and $y = -\frac{1}{2}x + 1$.
$\iint_R (3x^2 + 8xy + 4y^2) \, dx \, dy$
$\iint_R (3x^2 + 8xy + 4y^2) \, dx \, dy = ?$
(Simplify your answer.)