If we start from the origin, then the vector would be v = (52, 12) as given. But suppose we shift its initial point. Doing so would preserve its direction. For example, if we move its initial point to (1, 1), we'd have to shift its terminus by the same amount (1 unit to the right, 1 unit up) so that its terminal point would be (52 + 1, 12 + 1) = (53, 13).
Option A is not correct. If we want the vector to start at (52, 12), we have to adjust the terminus by the same distance by adding (52, 12) to the terminus. This means the resulting vector would start at (52, 12) and end at (52 + 52, 12 + 12) = (104, 24).
One important thing to observe here is that the difference between the terminal and initial points always returns v. In the first example: (53, 13) - (1, 1) = (52, 12). In checking option A: (104, 24) - (52, 12) = (52, 12). So to eliminate any other answer choices, all you need to do is subtract.
Option B is correct by this "rule". (66, 7) - (14, -5) = (52, 12).
Options C and D are not. (0, 12) - (52, 0) = (-52, 12), and (64, -4) - (-12, 16) = (76, -20).