2. In the Cartesian coordinate system, the area of the region formed by points $(x, y)$ satisfying $|x|+|y|+|x-2| \leqslant 4$ is
$\qquad$ (Supplied by An Zhenping)
2. 12 .

Obviously, the region is symmetric about the $x$-axis. Therefore, we only need to consider the graph represented by the equation $|x|+|y|+|x-2|=4$ when $y \geqslant 0$.

Draw the graph of the function $y=4-|x|-|x-2|(-1 \leqslant x \leqslant 3)$, and then reflect it about the $x$-axis, to obtain the graph represented by the equation $|x|+|y|+|x-2|=4$. As shown in Figure 5, the boundary and interior of this graph represent the region indicated by $|x|+|y|+|x-2| \leqslant 4$, and it is easy to calculate that its area is 12.