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\frac{2\sqrt{6}}{3\left(\sqrt{6}\right)^{2}}
Rationalize the denominator of \frac{2}{3\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.
\frac{2\sqrt{6}}{3\times 6}
The square of \sqrt{6} is 6.
\frac{\sqrt{6}}{3\times 3}
Cancel out 2 in both numerator and denominator.
\frac{\sqrt{6}}{9}
Multiply 3 and 3 to get 9.