I need the logic ( please don't ask why I entered 720 TT)

The key idea is of relative speed

Hour hand speed is 0.5°/min

Minute hand speed is 6°/min

Hence, relative speed = 5.5°/min

They are in straight line (opposite)

i.e. angle between them is 180°

Time between two such positions will be 180/5.5

We know that 12 hrs = 720 mins

So in 12 hrs they would meet 720/(180/5.5) = 22

But the ending point of hr 1 when they coincide and the starting point of hr 2

(double counted)

Hence in 12 hrs they would meet 22/2 = 11 times

In 24 hrs they would meet 11×2 = 22 times