jmc

The base of the hemisphere is a circle with radius 6 and area $6^2\pi =36\pi$. The curved top of the hemisphere has half the surface area of a full sphere, which has surface area $4\pi (6^2)=144\pi$, so the curved top of the hemisphere has $144\pi /2=72\pi$. The total surface area of the hemisphere is $36\pi +72\pi =\boxed{108\pi }$.