6. Find the maximum positive integer $m$, such that it is possible to fill each cell of an $m$ row by 8 column grid with one of the letters $C, G, M, O$, and the following property holds: for any two different rows in the grid, there is at most one column where the letters in these two rows are the same.
6. The largest $m=5$.

First, provide the construction, as shown in Table 1.
Table 1
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline $\mathrm{C}$ & $\mathrm{C}$ & $\mathrm{C}$ & $\mathrm{C}$ & $\mathrm{G}$ & $\mathrm{G}$ & $\mathrm{G}$ & $\mathrm{G}$ \\
\hline $\mathrm{C}$ & $\mathrm{G}$ & $\mathrm{G}$ & $\mathrm{G}$ & $\mathrm{C}$ & $\mathrm{C}$ & $\mathrm{C}$ & $\mathrm{M}$ \\
\hline $\mathrm{G}$ & $\mathrm{C}$ & $\mathrm{M}$ & $\mathrm{M}$ & $\mathrm{C}$ & $\mathrm{M}$ & $\mathrm{M}$ & $\mathrm{C}$ \\
\hline $\mathrm{M}$ & $\mathrm{M}$ & $\mathrm{C}$ & $\mathrm{O}$ & $\mathrm{M}$ & $\mathrm{C}$ & $\mathrm{O}$ & $\mathrm{C}$ \\
\hline $\mathrm{o}$ & $\mathrm{O}$ & $\mathrm{O}$ & $\mathrm{C}$ & $\mathrm{O}$ & $\mathrm{o}$ & $\mathrm{C}$ & $\mathrm{O}$ \\
\hline
\end{tabular}

Next, prove that $m \geqslant 6$ cannot satisfy the problem's requirements.
In fact, when $m=6$, it cannot satisfy the problem's requirements; when $m>6$, it is sufficient to consider any 6 rows to show that it cannot satisfy the problem's requirements.

Next, we only need to prove that $m=6$ cannot satisfy the problem's requirements.
For any integer $a$, it is clear that,
$$
\begin{array}{l}
(a-1)(a-2) \geqslant 0 \\
\Rightarrow a(a-1) \geqslant 2(a-1) \\
\Rightarrow \mathrm{C}_{a}^{2} \geqslant a-1 .
\end{array}
$$

Consider any column, and let the number of $C, G, M, O$ in this column be $a_{1}, a_{2}, a_{3}, a_{4}$, respectively. Then, by (1),
$$
\begin{array}{l}
\mathrm{C}_{a_{1}}^{2}+\mathrm{C}_{a_{2}}^{2}+\mathrm{C}_{a_{3}}^{2}+\mathrm{C}_{a_{4}}^{2} \\
\geqslant a_{1}-1+a_{2}-1+a_{3}-1+a_{4}-1=2 .
\end{array}
$$

This indicates that there are at least two "row pairs" (i.e., unordered pairs of two rows) such that the two rows in each pair have the same letter in this column.

Since $2 \times 8 > \mathrm{C}_{6}^{2}$, there exist two columns such that the row pairs corresponding to these two columns have overlaps. For this overlapping row pair, there are at least two columns where the two rows in this pair have the same letter, which is a contradiction.
In conclusion, the maximum value of $m$ is 5.