15. (6 points) As shown in the figure, the base radii of two cylindrical containers, A and B, are 2 cm and 3 cm, respectively. It is known that container A is full of water, and container B is empty. Now, all the water from container A is poured into container B, and the height of the water surface is $\frac{2}{3}$ less than 6 cm of the height of container A. Then the height of container A is $\qquad$ cm.
【Solution】Solution: Let the height of the container be $x$ cm, then the water depth in container $B$ is $\left(\frac{2}{3} x-6\right)$ cm. According to the problem, we can set up the equation:
$$
\begin{aligned}
3.14 \times 2^{2} \times x & =3.14 \times 3^{2} \times\left(\frac{2}{3} x-6\right) \\
3.14 \times 4 \times x & =3.14 \times 9 \times\left(\frac{2}{3} x-6\right), \\
4 x & =6 x-54 \\
2 x & =54 \\
x & =27
\end{aligned}
$$

Answer: The height of container A is 27 cm.
Therefore, the answer is: 27.