6. Point $N$ divides the diagonal $A C$ of trapezoid $A B C D$ in the ratio $C N: N A=4$. The lengths of the bases $B C$ and $A D$ of the trapezoid are in the ratio $2: 3$. A line is drawn through point $N$ and vertex $D$, intersecting the lateral side $A B$ at point $M$. What fraction of the area of the trapezoid is the area of quadrilateral $M B C N$?
Answer: $S_{\text {MBCN }}: S=124: 325$.

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