Minimum Value of Expression

Let $y = x + 4 > 0 \implies x = y - 4$. Expression = $\frac{3(y + 2)(y + 8)}{2y} = \frac{3(y^2 + 10y + 16)}{2y} = \frac{3}{2}\left(y + \frac{16}{y} + 10\right)$. By AM-GM, minimum of $y + \frac{16}{y}$ is $2\sqrt{16} = 8$. Minimum value = $\frac{3}{2}(8 + 10) = \frac{3}{2}(18) = 27$.