Simplify inside the parentheses and the absolute value symbols first. Then find absolute value, and use PEMDAS.

$\displaystyle{{\left({3}-{6}\right)}}^{{2}}-\frac{{{3}{\left|{5}-{9}\right|}}}{{2}}={{\left(-{3}\right)}}^{{2}}-\frac{{{3}{\left|-{4}\right|}}}{{2}}={{\left(-{3}\right)}}^{{2}}-\frac{{{3}\cdot{4}}}{{2}}={9}-\frac{{12}}{{2}}={9}-{6}={3}\usepackage{cmbright}\Huge\$