jmc

From ``$3$'' to ``$9$'' is a difference of 6 hours out of the 12 on the clock, so the hands are separated by $\frac{6}{12}=\frac{1}{2}$ of the degrees on the clock. From ``$2$'' to ``$10$,'' the smaller angle (clockwise from $10$ to $2$) is a difference of 4 hours out of 12 on the clock, so the hands are separated by $\frac{4}{12}=\frac{1}{3}$ of the degrees on the clock. The difference in the angles is $\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$ of the degrees on the clock. Since the clock has $360^{\circ }$, the angle decreases by $\frac{360}{6}=\boxed{60^{\circ }}$.