It means give logical reasons for whatever you are trying to justify.
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To justify something in math is to prove it. Example: Justify 4x = 8 when x = 2. When x = 2, 4(2) = 8. Done. By doing this I justified that 4x = 8 when x = 2.
It means that you are supposed to prove something.
You sound like you're going to fail math this year and trying to justify it.
In math terms, it means to prove your answer and make sure it is right.