Question

The phrase the difference between a number 2 can be written as which variable expression

Answer 1

\(|x-2|\)

Answer 2

The word "difference" refers to subtraction.
The difference between a number and 2 is (letting x denote the number): x - 2
If you want the *distance* between a number and 2 (so that the answer is always nonnegative) then you want: |x - 2| (which is the same as |2 - x|.

Answer 3

There's lot of "translating words to mathematical expression" stuff here:
http://www.onemathematicalcat.org/algebra_book/online_problems/translate_math_phrases.htm