Questions

The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.

The case where there is 6 months day, and 6 months night could only happen on poles because The Earth is tilted on its axis.

The pole which is away (opposite direction of sun) from the Sun remains in complete darkness till it comes in front of the sun.

So we conclude that, countries at the poles have 6 months day, and 6 months night.

So countries close to these region have such cases like, Alaska, Antarctica, Norway etc.

Norway, the northernmost inhabited region of Europe, there is no sunset from approximately 19 April to 23 August. The extreme sites are the poles, where the sun can be continuously visible for half the year. The North Pole has midnight sun for 6 months from late March to late September.