\[6;\ \ x;\ \ y;\ - 12\sqrt{2} \Longrightarrow\]
\[\Longrightarrow геометрическая\ \]
\[прогрессия \Longrightarrow\]
\[\Longrightarrow q = \frac{x}{6} = \frac{y}{x} = - \frac{12\sqrt{2}}{y}\]
\[\left\{ \begin{matrix} \frac{x}{6} = \frac{y}{x}\text{\ \ \ \ \ \ \ \ \ \ } \\ \frac{y}{x} = - \frac{12\sqrt{2}}{y} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} y = \frac{x^{2}}{6}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ } \\ x^{3} = - 432\sqrt{2} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} y = \frac{x^{2}}{6}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ x^{3} = \left( - \sqrt{72} \right)^{3} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} y = \frac{x^{2}}{6}\text{\ \ \ } \\ x = - \sqrt{72} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x = - 6\sqrt{2} \\ y = 12\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[Ответ:\ - 6\sqrt{2}\ \ \ и\ \ \ 12.\]