6. In Rt $\triangle A B C$, $\angle B=90^{\circ}, A B=$ $4, B C=2, D$ is any point inside $\mathrm{R} t \triangle A B C$, and through $D$ are drawn lines $E F, M N$, $P T$ parallel to the three sides of the triangle. Let $S$ be the sum of the areas of $\triangle D E P, \triangle D M F$ and $\triangle D N T$, then the minimum value of $S$ is
$\frac{4}{3}$