6. As shown in the figure, in $\triangle A B C$, $D, E$ are on $B C$, with $B D: D E: E C=3: 2: 1$. Point $M$ is on $A C$, with $C M: M A=1: 2$. $B M$ intersects $A D, A E$ at $H, G$. Then $B H: H G: G M$ equals ( . ).
(A) $3: 2: 1$
(B) $5: 3: 1$
(C) $25: 12: 5$
(C) $51: 24: 10$
6. D (Hint,

Draw $M N / / B C$ intersecting $A D, A E$ at $Q, P$. Let $B H=x, H G=$ $y, G M=z$, then we have $\frac{x}{y+z}=\frac{B D}{M Q}=\frac{D C}{M Q}=\frac{3}{2}, \frac{x+y}{z}=\frac{B E}{M P}=\frac{5 E C}{M P}=\frac{5 \cdot 3}{2}$. Solving these equations simultaneously gives $x: y: z=51: 24: 10.$)