How would I get the answer to this SAT math subject level 1 question?

Subtract the first given equation from the second given equation:
(x-2)^2 - x^2 = 0
Expand:
x^2 - 4x + 4 - x^2 = 0
Combine like terms:
4x = 4
x = 1
Substitute this value for x into x^2 + y^2 = 4 and solve for y:
1 + y^2 = 4
y^2 = 3
y = ± √3
So the two points of intersection are:
(1, - √3) and (1, √3)

(1, √3) and (1, -√3)

You didn't post the possible answers. "which of the following..." suggests there will be a list.
So, look at the values you didn't post and try a few of them. You could also consider what these circles look like. The first is centered at the origin and has a radius of 2
The second is centered at (2,0) and also has a radius of 2.
Where will they intersect?