You can use the given sides to find: $\displaystyle{\tan{{M}}}=\frac{{8}}{{8}}={1}\usepackage{cmbright}\Huge\$

Refer to the $\displaystyle{{45}}^{\circ}-{{45}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle. From there you can see that $\displaystyle{{\tan{{45}}}}^{\circ}={1}\usepackage{cmbright}\Huge\$ . It follows that $\displaystyle{m}\angle{M}={{45}}^{\circ}\usepackage{cmbright}\Huge\$ . Use the definition of sine:

$\displaystyle\frac{{8}}{{n}}={\sin{{M}}}={{\sin{{45}}}}^{\circ}=\frac{{\sqrt{{2}}}}{{2}}\usepackage{cmbright}\Huge\$

This implies that: $\displaystyle\sqrt{{{2}}}\cdot{n}={8}\cdot{2}\Rightarrow{n}=\frac{{{8}\cdot{2}}}{\sqrt{{2}}}={8}\sqrt{{2}}\usepackage{cmbright}\Huge\$