2. As shown in Figure $1, M_{1}$, $M_{2}$, $M_{3}$, $M_{4}$ are points on the sides $AB$, $BC$, $CD$, $DA$ of quadrilateral $ABCD$, respectively, and $AM_{1}: M_{1}B = AM_{4}: M_{4}D = CM_{2}: M_{2}B = CM_{3}: M_{3}D = 1:2$. $P$ is a point inside quadrilateral $ABCD$, and the sum of the areas of quadrilaterals $PM_{1}AM_{4}$ and $PM_{2}CM_{3}$ is 8. Then the area $S$ of quadrilateral $ABCD$ is ( ).
(A) 16
(B) 24
(C) 20
(D) 32
2. B.

As shown in Figure 5, connect $P A$,
$P B, P C, P D$.
Given $A M_{1}: M_{1} B=$
$1: 2$, it is easy to see that
$$
A B=3 A M_{1} .
$$

Thus, $S_{\triangle P A B}=3 S_{\triangle P A M_{1}}$.
Similarly, $S_{\triangle P B C}=3 S_{\triangle P C M_{2}}, S_{\triangle P C D}=3 S_{\triangle P C M_{3}}$,
$$
S_{\triangle P A D}=3 S_{\triangle P A M_{4}} \text {. }
$$

Adding the above four equations, we get