Step-by-Step Solution:
1. Start with the original equation:

$$
\(3 x m+2 y m-2 y n-3 x n=0\)
$$

2. Group the terms by common variables ( $m$ and $n$ ):

$$
\((3 x m+2 y m)-(3 x n+2 y n)=0\)
$$

3. Factor out $m$ from the first group and $n$ from the second group:

$$
\(m(3 x+2 y)-n(3 x+2 y)=0\)
$$

4. Factor out the common binomial $\((3 x+2 y)\)$ :

$$
\((3 x+2 y)(m-n)=0\)
$$

5. Use the condition $m \neq n$ :

For the product of two terms to be zero, at least one of the terms must be zero. Since we are given that $m \neq n$, then $m-n$ cannot be zero. Therefore, the other term must be zero:

$$
\(3 x+2 y=0\)
$$

\(\begin{aligned}
&\text { 6. Solve for } y \text { : }\\
&\begin{aligned}
2 y & =-3 x \\
y & =-\frac{3 x}{2}
\end{aligned}
\end{aligned}\)