6. In an $8 \times 8$ grid, each cell is colored either white or black. To ensure that from any $2 \times 3$ or $3 \times 2$ rectangle selected in the grid, there are always two adjacent black cells, how many cells at least need to be colored black?
6. At least 24 cells in the grid need to be colored black.

First, we prove that in any valid coloring, at least two of the four cells $A, B, C, D$ in a "cross" (as shown in Figure 10) must be colored black. Otherwise, if at most one of these cells is black, then at least three cells are white. Suppose, without loss of generality, that $A, B, C$ are white, then in the $2 \times 3$ rectangle shown in Figure 11, there would be no two black cells with a common edge, which is a contradiction.

Next, using the above conclusion, consider the 12 crosses shown in Figure 12. Each cross must have at least 2 cells colored black, which means that the original grid must have at least $2 \times 12 = 24$ black cells. In fact, as shown in Figure 13, this coloring method satisfies the problem's requirements.

In summary, at least 24 cells in the grid need to be colored black.