6. Find all pairs $(x, y)$ such that for each pair of values, the numbers
$u=\sqrt{4+x^{3}-9 x}-x-3^{y}$ and $v=2-x-3^{y}$ satisfy the following three conditions:
(1) If $|u|>|v|$, then $u>0$;
(2) If $|u|v$;
(3) If $|u|=|v|$, then $u>0>v$.

保留了源文本的换行和格式。
6. Three conclusions hold simultaneously
$$
\begin{array}{l}
\Leftrightarrow u>v \\
\Leftrightarrow \sqrt{4+x^{3}-9 x}>2 \\
\Leftrightarrow 4+x^{3}-9 x>4 \\
\Leftrightarrow x(x-3)(x+3)>0 \\
\Leftrightarrow-33 .
\end{array}
$$

Therefore, $-33$, and $y$ can be any number.