It is easier for me to explain with a few numbers.
The average for the first four quarters in the question is (900 + 1100 + 1200 + 1000) / 4 = 1050. In the same way, the average for the second lot of four quarters is (1100 + 1200 + 1000 + 1050) / 4 = 1087.5
However, both of these averages are sort of in the middle of the year and do not correspond to any one quarter. To centre it, you take the average of the two – (1050 + 1087.5) / 2 = 1068.75
(In this exam question you did not actually have to calculate it because the examiner had done the arithmetic for you)