From the time shown, when will the REFLEX angle between the hands first be 250°?

A reflex angle of $250^{\circ }$ means the smaller angle is $110^{\circ }$. From 12:00 the minute hand gains $5.5^{\circ }$/min: $\frac{110}{5.5}=20$ min, so 12:20. (At 12:40 the hands are $140^{\circ }$ apart, a reflex angle of $220^{\circ }.$)