First use the power property, then use the quotient property:

$\displaystyle{\log}_{{{4}}}{{\left(\frac{{64}}{{a}}\right)}}^{{2}}={2}\cdot{\log}_{{{4}}}{\left(\frac{{64}}{{a}}\right)}={2}{\left({\log}_{{{4}}}{64}-{\log}_{{{4}}}{a}\right)}\usepackage{cmbright}\Huge\$

$\displaystyle={2}{\left({3}\right)}-{2}{\log}_{{{4}}}{a}={6}-{2}{\log}_{{{4}}}{a}\usepackage{cmbright}\Huge\$