You can use the given sides to find: $\displaystyle{\sin{{M}}}=\frac{{4}}{{8}}=\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$

Refer to the $\displaystyle{{30}}^{\circ}-{{60}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle. From there you can see that $\displaystyle{{\sin{{30}}}}^{\circ}=\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ . It follows that $\displaystyle{m}\angle{M}={{30}}^{\circ}\usepackage{cmbright}\Huge\$ . Use the definition of cosine:

$\displaystyle\frac{{p}}{{8}}={\cos{{M}}}={{\cos{{30}}}}^{\circ}=\frac{\sqrt{{3}}}{{2}}\usepackage{cmbright}\Huge\$

This implies that: $\displaystyle{2}{p}={8}\sqrt{{3}}\Rightarrow{p}={4}\sqrt{{3}}\usepackage{cmbright}\Huge\$