Solve the given inequality for real $x: 3(2-x) \geq 2(1-x)$
$3(2-x) \geq 2(1-x)$
$\Rightarrow 6-3 x \geq 2-2 x$
$\Rightarrow 6-3 x+2 x \geq 2-2 x+2 x$
$\Rightarrow 6-x \geq 2$
$\Rightarrow 6-x-6 \geq 2-6$
$\Rightarrow x \leq 4$
Thus, all real numbers $x$, which are less than or equal to 4 , are the solutions of the given inequality.
Hence, the solution set of the given inequality is $(-\infty, 4]$.