Simplify each radical and then subtract like terms:

$\displaystyle{6}\sqrt{{{75}}}-{4}\sqrt{{{12}}}={6}\sqrt{{{25}\cdot{3}}}-{4}\sqrt{{{4}\cdot{3}}}={6}\sqrt{{25}}\cdot\sqrt{{3}}-{4}\sqrt{{4}}\cdot\sqrt{{3}}\usepackage{cmbright}\Huge\$

$\displaystyle={6}\cdot{5}\sqrt{{{3}}}-{4}\cdot{2}\sqrt{{{3}}}={30}\sqrt{{{3}}}-{8}\sqrt{{{3}}}={\left({30}-{8}\right)}\sqrt{{3}}={22}\sqrt{{3}}\usepackage{cmbright}\Huge\$