Solution
Rationalizing the denominator,
[tex]\begin{gathered} \frac{12}{\sqrt{x}-\sqrt{x-6}}\times\frac{\sqrt{x}+\sqrt{x-6}}{\sqrt{x}+\sqrt{x-6}}=\frac{12(\sqrt{x}+\sqrt{x-6})}{(\sqrt{x}-\sqrt{x-6})(\sqrt{x}+\sqrt{x-6})} \\ \\ =\frac{12(\sqrt{x}+\sqrt{x-6})}{x-(x-6)}=\frac{12(\sqrt{x}+\sqrt{x-6})}{x-x+6}=\frac{12(\sqrt{x}+\sqrt{x-6})}{6}=2(\sqrt{x}+\sqrt{x-6}) \end{gathered}[/tex]
The correct option is C.
