Factor out perfect squares: $\displaystyle\sqrt{{{4}\cdot{4}\cdot{3}\cdot{{x}}^{{2}}\cdot{{y}}^{{2}}\cdot{y}}}\usepackage{cmbright}\Huge\$

Separate the factors into individual radicals: $\displaystyle\sqrt{{{{4}}^{{2}}}}\cdot\sqrt{{{3}}}\cdot\sqrt{{{{x}}^{{2}}}}\cdot\sqrt{{{{y}}^{{2}}}}\cdot\sqrt{{{y}}}\usepackage{cmbright}\Huge\$

Find the square roots: $\displaystyle{4}\cdot\sqrt{{{3}}}\cdot{\left|{x}\right|}\cdot{\left|{y}\right|}\cdot\sqrt{{{y}}}\usepackage{cmbright}\Huge\$

Simplify: $\displaystyle{4}{\left|{x}{y}\right|}\sqrt{{{3}{y}}}\usepackage{cmbright}\Huge\$