Let's evaluate each statement regarding the opposite of -12, which is 12.
A. The opposite of -12 is -1/12.
This statement is false. The opposite of -12 is 12, not -1/12.
B. -12 and its opposite are located on the same side of zero on a number line.
This statement is false. -12 is on the left side of zero, while its opposite, 12, is on the right side of zero.
C. -12 and its opposite are located the same distance from zero on a number line.
This statement is true. Both -12 and 12 are 12 units away from zero.
D. The opposite of the opposite of -12 is -12.
This statement is false. The opposite of -12 is 12, and the opposite of 12 is -12. So, the statement should say that the opposite of the opposite of -12 is 12.
In summary, only statement C is true.