[tex]\frac{6 \sqrt{3}}{\sqrt{3} - \sqrt{2}} = \frac{6 \sqrt{3}}{\sqrt{3} - \sqrt{2}} \times \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} = \frac{(6 \sqrt{3})(\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})} [/tex]
[tex]= \frac{6 \sqrt{9} + 6 \sqrt{6}}{\sqrt{9} + \sqrt{6} - \sqrt{6} - \sqrt{4}} [/tex]
[tex]= \frac{6 \sqrt{9} + 6 \sqrt{6}}{\sqrt{9} - \sqrt{4}} = \frac{6 \times 3 + 6 \sqrt{6}}{3 - 2} = \frac{18 + 6 \sqrt{6}}{1} = 18 + 6 \sqrt{6} [/tex]