To find the coordinates of A' and B' after a dilation with a scale factor of 12 1/2, centered at the origin, we can multiply the x and y coordinates of each point by the scale factor.
For point A(-6, 4), the x-coordinate becomes -6 * 12 1/2 = -6 * 25/2 = -150/2 = -75, and the y-coordinate becomes 4 * 12 1/2 = 4 * 25/2 = 100/2 = 50. So the coordinates of A' are (-75, 50).
For point B(-8, 2), the x-coordinate becomes -8 * 12 1/2 = -8 * 25/2 = -200/2 = -100, and the y-coordinate becomes 2 * 12 1/2 = 2 * 25/2 = 50/2 = 25. So the coordinates of B' are (-100, 25).
Therefore, the coordinates of A' and B' are (-75, 50) and (-100, 25) respectively.