6. (5 points) As shown in the figure, quadrilateral $ABCD$ is a square, $ABGF$ and $FGCD$ are both rectangles, point $E$ is on $AB$, and $EC$ intersects $FG$ at point $M$. If $AB=6$, and the area of $\triangle ECF$ is 12, then the area of $\triangle BCM$ is $\qquad$
【Solution】Solution: According to the analysis, given that the area of $\triangle E C F$ is 12, we know that $\frac{1}{2} \times F M \times B G + \frac{1}{2} \times F M \times C G = 12$,
$$
\begin{array}{l}
\Rightarrow \frac{1}{2} \times F M \times(B G+G C)=\frac{1}{2} \times F M \times B C=12 \\
\Rightarrow F M=\frac{2 \times 12}{B C}=\frac{24}{6}=4, \\
\Rightarrow M G=6-4=2,
\end{array}
$$
$\therefore$ The area of $\triangle B C M$: The area of $\triangle E C F$ $=M G: F M=2: 4=1: 2$,
$\therefore$ The area of $\triangle B C M$ $=\frac{1}{2} \times$ The area of $\triangle E C F$ $=\frac{1}{2} \times 12=6$.
Therefore, the answer is: 6