It would be a good idea to start with the definition of "absolute value": |x|= x if x is greater than or equal to 0, |x|= -x if x is less than 0.
So |2n|= 2n if n is greater than or equal to 0, |2n|= -2n if x< 0.
Case 1: if n is greater than or equal to 0, then |2n|= 2n= 6 so n= 3. That is positive so is a valid solution.
Check: 2(3)= 6 which is positive so |2(3)|= |6|= 6.
Case 2: if n< 0, then |2n|= -2n= 6 so n= -3. That is negative so is a valid solution.
Check: 2(-3)= -6 which is negative so |2(-3)|= |-6|= 6.
The two numbers, 3 and -3, satisfy |2n|= 6.