First simplify by applying the distributive property. Then combine like terms.

$\displaystyle{12}{{y}}^{{2}}-{3}{\left({8}{{y}}^{{2}}-{6}{x}{{y}}^{{2}}\right)}+{4}{y}{\left({9}{y}-{7}{x}{y}\right)}={12}{{y}}^{{2}}-{24}{{y}}^{{2}}+{18}{x}{{y}}^{{2}}+{36}{{y}}^{{2}}-{28}{x}{{y}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle={\left({12}-{24}+{36}\right)}{{y}}^{{2}}+{\left({18}-{28}\right)}{x}{{y}}^{{2}}={24}{{y}}^{{2}}-{10}{x}{{y}}^{{2}}\usepackage{cmbright}\Huge\$