2021 Fall AMC 10A Problem 18

There are $2$ cases. Case $1:$ the top-right and bottom-left sections have the same crop There are $4$ options for which crop is in those sections. The other two sections have $3$ options for the crop since each crop has one restriction for crops next to it. This gives us $$4 \cdot 3 \cdot 3 = 36$$ combinations. Case $2:$ the top-right and bottom-left sections have different crops There are $4$ options for the top-right crop and $3$ different options for the bottom-left crop. Each of the other two sections borders both of these crops, leaving $2$ choices for each. This gives us another $$4 \cdot 3 \cdot 2 \cdot 2 = 48$$ configurations. In total, there are $36 + 48 = 84$ combinations. Thus, C is the correct answer.