Subtract 4 from both sides: $\displaystyle{{\left({x}-{4}\right)}}^{{2}}={32}\usepackage{cmbright}\Huge\$

Use the Square Root Property: $\displaystyle{x}-{4}=\pm\sqrt{{32}}\usepackage{cmbright}\Huge\$

Add 4 to both sides: $\displaystyle{x}={4}\pm\sqrt{{32}}\usepackage{cmbright}\Huge\$

Simplify the radical: $\displaystyle{x}={4}\pm\sqrt{{{16}\cdot{2}}}={4}\pm{4}\sqrt{{2}}\usepackage{cmbright}\Huge\$