The line $2x + 3y = 6$ can be parametrized through the point $(3, 0)$ as $x = 3 - 3t, y = 2t$ for integer parameter $t$. How many integer solutions $(x, y)$ satisfy both $2x + 3y = 6$ and the bounds $|x| \leq 5, |y| \leq 4$?