if the equation of a circle is (x  - 2)2  + (y  - 6)2  = 4, it passes through point (2, 8)(5, , 6)(2, -8)

What you need to do is to plug the x and y value into the equation to see which one works.
(2-2)²+(8-6)²=0+4=4
so (2,8) is the answer.
Make sure by plugging in the other three pairs of values. You'll see that only (2,8) works.