By supplementary angles, we have
[tex]m\angle KOM+m\angle MOP=180[/tex]Let's replace each expression.
[tex]4x-4+2x-2=180[/tex]Now, we solve for x.
[tex]\begin{gathered} 6x-6=180 \\ 6x=180+6 \\ x=\frac{186}{6} \\ x=31 \end{gathered}[/tex]Once we know the value of the variable, we find angle MOP.
[tex]\begin{gathered} m\angle MOP=2x-2=2\cdot31-2=62-2 \\ m\angle MOP=60 \end{gathered}[/tex]