Answer
$$6$$
Work Step by Step
Dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction.
$$\frac{\frac{9}{m-n}}{\frac{3}{2m-2n}}=\frac{9}{(m-n)}\times \frac{(2m-2n)}{3}$$
Factor each term:
$$\frac{3\times 3}{(m-n)}\times \frac{2(m-n)}{3}.$$
Cancel common factors:
$$3\times 2=6.$$