jmc

In the diagram, the radius of the sector is 12 so $OA=OB=12$. Since the angle of the sector is $60^{\circ }$, then the sector is $\frac{60^{\circ }}{360^{\circ }}=\frac{1}{6}$ of the total circle. Therefore, arc $AB$ is $\frac{1}{6}$ of the total circumference of a circle of radius 12, so has length $\frac{1}{6}(2\pi (12))=4\pi$. Therefore, the perimeter of the sector is $12+12+4\pi =\boxed{24+4\pi }$.