6. In an $m$ row, $n$ column grid, there are $m n$ small squares with a side length of 1. Each small square is colored with one of three colors: red, yellow, or blue. It is known that each row of the grid has 6 red small squares, each column has 8 yellow small squares, and the entire grid has 15 blue small squares. If $n$ is a two-digit prime number, then, $m=$ $\ldots, n=$ $\qquad$ .
$$
\text { 6. } m=17, n=13 \text {. }
$$

From the problem, we have $6 m+8 n+15=m n$. Therefore,
$$
\begin{array}{l}
(m-8)(n-6)=48+15=63 \\
=1 \times 63=3 \times 21=7 \times 9 .
\end{array}
$$

Since $n$ is a two-digit prime number, we have $n=13, m=17$.