SOLUTION: insert eight arithmetic mean between 26 and -10

In the number line, you have this segment  [-10,26]  of the length  10 + 26 = 36.


They want you insert 8 numbers (8 points in the number line) to divide this segment in 9 (nine) equal parts.


I am sure that you do understand why I am talking about 9 parts: because 9 = 8 + 1.


Next, it is clear for you, that each part must be  36/9 = 4 units long.


It means that your points (numbers) are the terms of an arithmetic progression
with the first term of -10 and the common difference of 4


    -10, -6, -2, 2, . . . 


and you can continue it further till 26.


Then the term of this progression, excluding its endpoints, give you the answer to the problem's question.