What is the center of the circle that has a diameter whose endpoints are (6, -4) and (18, 10)?

The center of the circle is the mid-point of every diameter.

When you have the (x,y) coordinates of the ends of a line segment,
the 'x' coordinate of the midpoint is the average of the 'x' coordinates
at the ends, and the 'y' coordinate of the midpoint is the average of the
'y' coordinates at the ends.

   x(mid) = 1/2 (6 + 18) = 1/2 (24)  =  12

   y(mid) = 1/2 (-4 + 10) = 1/2 (6)  =  3

The center of the circle is the point  (12, 3) .

Cis your correct answer