4. (20 points) The ballroom in the palace of the thirtieth kingdom is a region on the plane, the coordinates of which satisfy the conditions $|x| \leqslant 4,|y| \leqslant 6$. How many identical parquet tiles, having the shape of a rectangle with sides 1.5 and 2, are needed to tile the floor of the room? Tiling is considered to be laying without gaps, without overlaps, and not extending beyond the boundaries of the area.
Answer: 32.

Solution: From the condition, we find that the magic room is a rectangle with sides parallel to the coordinate axes, and the lengths of the sides parallel to the x-axis are 8, while the lengths of the sides parallel to the y-axis are 12. It is not hard to see that a tiling exists (along the side of the room with length 12, an integer number of tiles with side length 1.5 can be placed; and, obviously, along the side of the room with length 8, an integer number of tiles with side length 2 can also be placed). The area of the room is $8 \times 12 = 96$, and the area of one tile is $1.5 \times 2 = 3$. Therefore, we get that a total of $96 \div 3 = 32$ tiles are required.