The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 o clock only. Hence the hands point in the opposite directions 22 times in a day.

The hands of a clock coincide(0° between them) 11 times in every 12 hours (between 11 and 1, they coincide only once, at 12 oclock). Hence the hands coincide 22 times in a day.

So In 24 hours, the hands come in opposite direction or coincide 44 times.

This is already given as a formula and its is better to learn the answer by heart as 44

which can save time in competitive exams.(However you should know the theory behind).