For best alignment,

use \left\{ and \right. with the aligned environment

instead of cases wrapped in align*.

\begin{equation*} \left\{ \begin{aligned} 2 x_1 + 4 x_2 & \geq 12 \\ 5 x_1 + 3 x_2 & \geq 15 \\ 4 x_1 + x_2 & \geq 8 \end{aligned} \right. \end{equation*}