6. In a tetrahedron $ABCD$ with volume 12, points $E, F, G$ are on edges $AB, BC, AD$ respectively, and $AE = 2EB, BF = FC, AG = 2GD$. A section $EFHG$ is made through points $E, F, G$. The distance from point $C$ to this section is 1. Then the area of this section is $\qquad$ .