If (2x + 12) is perfectly divisible by x, then (2x + 12)/x has to be an integer as x is an integer.
Now if we divide, the expression simplifies to (2 + 12/x). The only way in which this expression would be an integer is when 12/x is an integer or if 12 is perfectly divisible by x.
This is possible if x takes either of these values : 1, 2, 3, 4, 6, 12.
Hence the answer is 6 values.
Option C is Correct Answer