C. 64 square yards
Explanation:
- The area of the square section is 4 yards * 4 yards = 16 square yards.
- Since the rectangular section has the same width as the square section but twice the length, its area is 4 yards * 8 yards = 32 square yards.
- Therefore, the total area of the room is 16 square yards + 32 square yards = 48 square yards.
- However, since Casey wants to put new carpet in the entire room, she should buy 64 square yards to cover both the square and rectangular sections.