Correct. Plugging in (-2, 6) to $\displaystyle{\left({x},{y}\right)}\usepackage{cmbright}\Huge\$ yields two true statements:

$\displaystyle{6}\ge-\frac{{2}}{{3}}{\left(-{2}\right)}+{1}\usepackage{cmbright}\Huge\$

$\displaystyle{2}{\left(-{2}\right)}+{\left(-{6}\right)}>{1}\usepackage{cmbright}\Huge\$

All other points yield at least one false statement, so (-2, 6) is the solution.