6. Solve the congruence $111 x \equiv 75(\bmod 321)$.
6. Since $(111,321) \equiv 3$, and $3 \mid 75$, the congruence has 3 solutions.

First, solve the congruence $37 x \equiv 25(\bmod 107)$.
$$
x \equiv \frac{75}{111} \equiv \frac{-32}{4} \equiv -8 \equiv 99(\bmod 107),
$$

Thus, $x \equiv 99, 206, 313(\bmod 321)$ are the solutions.