[tex]\displaystyle \frac{6 \sqrt{6} }{3 \sqrt{6} -4 \sqrt{3} } = \frac{6 \sqrt{6} (3 \sqrt{6} +4 \sqrt{3} )}{54-48} = \frac{108+24 \sqrt{18} }{6} = \frac{108+24 \cdot 3 \sqrt{2} }{6} = \\ \\ = \frac{108+72 \sqrt{2} }{6} = \frac{\not6(18+12 \sqrt{2} )}{\not6} =18+12 \sqrt{2} [/tex]
