To calculate the degree of rotation of the hour hand between 8 o`clock in the morning and 2 o`clock in the afternoon, we need to determine the elapsed time.

From 8 o`clock in the morning to 2 o`clock in the afternoon, a total of 6 hours have passed.

In a 12-hour clock, the hour hand completes a full rotation of 360 degrees in 12 hours, which means it rotates 30 degrees per hour (360 degrees / 12 hours).

Therefore, in 6 hours, the hour hand will rotate:

Degree of rotation = (Number of hours) x (Degrees per hour)

= 6 hours x 30 degrees/hour

= 180 degrees

So, the hour hand will rotate 180 degrees between 8 o`clock in the morning and 2 o`clock in the afternoon. The correct answer is option D.