G4.3 It is given that $m$ and $n$ are two natural numbers and both are not greater than 10 . If $c$ is the number of pairs of $m$ and $n$ satisfying the equation $m x=n$, where $\frac{1}{4}<x<\frac{1}{3}$, find $c$.
$$
\begin{array}{l}
\frac{1}{4}0 \\
3 m-n<0
\end{array}\right. \\
3 m<n<4 m \\
1 \leq m \Rightarrow 3 \leq 3 m<n<4 m \leq 4 \times 10=40
\end{array}
$$

Possible $n=4,5,6, \ldots, 10$
when $n=4, \frac{4}{4}<m<\frac{4}{3}$ no solution when $n=5, \frac{5}{4}<m<\frac{5}{3}$ no solution when $n=6, \frac{6}{4}<m<\frac{6}{3}$ no solution when $n=7, \frac{7}{4}<m<\frac{7}{3} \Rightarrow m=2, x=\frac{2}{7}$ when $n=8, \frac{8}{4}<m<\frac{8}{3}$ no solution when $n=9, \frac{9}{4}<m<\frac{9}{3}$ no solution when $n=10, \frac{10}{4}<m<\frac{10}{3} \Rightarrow m=3, x=\frac{3}{10}$ $c=2$ (There are 2 solutions.)