6. In the $4 \times 4$ grid shown in Figure 5, draw " $\times$ " in two cells. Different ways are considered the same if they can be made identical through rotation. Figures 5 and 6 represent one way; Figures 6 and 7 are different, as Figure 7 can be obtained by flipping but not by rotating Figure 6.
How many different ways are there to draw two $\times$?
(A) 21
(B) 30
(C) 32
(D) 34
(E) 36
6. C.

Divide this coloring method into two categories: one that requires four rotations to coincide with itself, and another that coincides with itself after two rotations. Among these, the second category has only four cases as shown in Figure 13. Therefore, the total number sought is $\frac{\mathrm{C}_{16}^{2}-4 \times 2}{4}+4=32$.