9. $x, y \in \mathbf{R}^{+}, 3x+2y=12, xy$ 的最大值为

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.

9. $x, y \in \mathbf{R}^{+}, 3x+2y=12, xy$'s maximum value is
9. 6. $x y=\frac{1}{6}(3 x)(2 y) \leqslant \frac{1}{6} \cdot\left(\frac{3 x+2 y}{2}\right)^{2}=6$.