The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. To find the midpoint, we average the x-coordinates and the y-coordinates of the two endpoints.
The coordinates (8, 3) are the average of the x-coordinates of the two endpoints in the answer choice **(10, 0) and (6, 6)**.
```
x-coordinate: (10 + 6) / 2 = 8
y-coordinate: (0 + 6) / 2 = 3
```
The other answer choices do not have the same average x- and y-coordinates as (8, 3). Therefore, the only pair of coordinates that has a midpoint of (8, 3) is **(10, 0) and (6, 6)**.
So the answer is **(10, 0) and (6, 6)**.