Suppose that n is an integer such that n/3 is 12 greater than n/2 . which of the following is the value of n ?

You said that                                 n/3           =  n/2 + 12 .

There's only one number that 'n' can be.
It may or may not be an integer.  We'll have to see.

Subtract  n/2  from each side:      n/3 - n/2  =            12

Multiply each side by  12 :            4n  -  6n  =           144

Do the subtraction on the left:            -  2n  =           144

Divide each side by  -2 :                          n    =         - 72

Yep.  It turns out that 'n' is an integer.
It didn't have to be, just because you said so.
For example, if you said that  n/3  is only
11 greater than  n/2 , we could figure out
what number 'n' must be, and it wouldn't
be an integer.