Renaming is the same thing as borrowing. If the problem was 62 - 35 you would have to rename the 2 ....12...by borrowing from the 6.which would become 5.
In your example there is no need to rename since 65 - 32 can be subtracted without borrowing.
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sum means the answer of a math problem
in math terms reduce means to simplify
It is an abbreviation for quart.
Justification in math terms means to show how you solved the math problem. Lay out the problem and show step-by-step how the problem is solved.