It appears that you did not distribute $\displaystyle\sqrt{{{6}}}\usepackage{cmbright}\Huge\$ to both terms in the numerator. The first two steps are:

$\displaystyle\frac{{\sqrt{{{2}}}+\sqrt{{{3}}}}}{\sqrt{{{6}}}}\cdot\frac{\sqrt{{{6}}}}{\sqrt{{{6}}}}=\frac{{{\left(\sqrt{{{2}}}+\sqrt{{{3}}}\right)}{\left(\sqrt{{{6}}}\right)}}}{{{\left(\sqrt{{{6}}}\right)}{\left(\sqrt{{{6}}}\right)}}}=\frac{{\sqrt{{{12}}}+\sqrt{{{18}}}}}{\sqrt{{{36}}}}\usepackage{cmbright}\Huge\$

Then simplify radicals.