8. In an $8 \times 6$ grid, each cell is colored one of four colors: red, blue, yellow, or green. If each $2 \times 2$ subgrid contains exactly one cell of each color, the coloring is called "balanced." The number of different balanced colorings is $\qquad$ kinds.
8. 1896.

Balanced coloring as shown in Figure 5.
If the four cells in the first $2 \times 2$ sub-square are colored with $A, B, C, D$ respectively, then the two cells in the third column above can only be colored with $A, C$.

If the first cell in the third column is colored with $C$, then the second cell in the third column is colored with $A$, and then the second cell in the third row can only be colored with $B$, the first cell in the third row can only be colored with $A$, and the third cell in the third row can only be colored with $C$, ... and so on. In a balanced coloring, in each column (or row), only two colors alternate, and in the adjacent two columns (or rows), the other two colors alternate.

When two colors alternate in each column, the first column selects two colors, and then each column selects the first color, there are $\mathrm{C}_{4}^{2} 2^{8}$ coloring methods; when two colors alternate in each row, similarly, there are $\mathrm{C}_{4}^{2} 2^{6}$ coloring methods.

There are $\mathrm{A}_{4}^{4}=24$ repeated cases, so the number of different coloring methods is $\mathrm{C}_{4}^{2} 2^{8}+\mathrm{C}_{4}^{2} 2^{6}-24=1896$.