You may have correctly used the quotient rule to get

$\displaystyle{\log}_{{{4}}}{\left(\frac{{{64}{x}}}{{{16}{y}}}\right)}={\log}_{{{4}}}{64}{x}-{\log}_{{{4}}}{16}{y}\usepackage{cmbright}\Huge\$ , and then used the product rule. But you probably forgot to distribute the minus sign when rewriting $\displaystyle{\log}_{{4}}{16}{y}\usepackage{cmbright}\Huge\$ as $\displaystyle{\log}_{{{4}}}{16}+{\log}_{{{4}}}{y}\usepackage{cmbright}\Huge\$ .