9. (6 points) As shown in the figure, the area of $\triangle A B C$ is 36, point $D$ is on $A B$, $B D=2 A D$, point $E$ is on $D C$, $D E=2 E C$, then the area of $\triangle B E C$ is $\qquad$ .
【Analysis】(1) The area of $\triangle A B C$ is $36, B D=2 A D$. According to the property that the area of a triangle is proportional to the base when the height is constant, we can derive: the area of $\triangle A B C$: the area of $\triangle B D C$ = 3: 2, so: the area of $\triangle B D C$ is: 36 $\times 2 \div 3=24$;
(2) The area of $\triangle B D C$ is $36 \times 2 \div 3=24, D E=2 E C$. According to the property that the area of a triangle is proportional to the base when the height is constant, we can derive: the area of $\triangle B E C$: the area of $\triangle B D C$ = 1: 3, so the area of $\triangle B E C$ is 24 $\div 3=8$.

【Solution】Solution: Since $B D=2 A D$, according to the property that the area of a triangle is proportional to the base when the height is constant, we can derive: the area of $\triangle A B C$: the area of $\triangle B D C$ = 3: 2, hence the area of $\triangle B D C$ is $36 \times 2 \div 3=24$; since $D E=2 E C$, similarly, we can derive: the area of $\triangle B E C$: the area of $\triangle B D C$ = 1: 3, hence the area of $\triangle B E C$ is $24 \div 3=8$.

Answer: The area of $\triangle B E C$ is 8.
Therefore, the answer is: 8.