jmc

Since we want to minimize the amount of fence that we use, we should have the longer side of the rectangle have one side as the wall. The grazing area is a $36$m by $60$m rectangle, so the $60$m side should be parallel to the wall. That means the two fences perpendicular to the wall are $36$m. We can start by counting $60÷12+1$ on the $60$m fence (since we also count the $0$m post). Next, we have the two $36$m fences. There are a total of $36÷12+1-1$ fences on that side since the $0$m and $60$m fence posts are also part of the $36$m fences. So we have $6+2\cdot 3=12$ minimum fence posts needed to box a $36$m by $60$m grazing area, or answer $\boxed{12}$.