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In the number line, you have this segment [-18,4] of the length 18 + 4 = 22 units.
They want you insert 3 numbers (3 points in the number line) to divide this segment in 4 (four) equal parts.
I am sure that you do understand why I am talking about 4 parts: because 4 = (3-1) + 2.
Next, it is clear for you, that each part must be 22/4 = 5.5 units long.
It means that your points (numbers) are the terms of an arithmetic progression
with the first term of -18 and the common difference of 5.5
-18, -12.5, -7, -1.5, 4. (*)
So, the three arithmetic means that you insert are the numbers -12.5, -7, -1.5.
In other words, the terms of this progression (*), excluding its endpoints, give you the answer to the problem's question.
Solved.
