I'm going to assume the circle is centered at the origin. You can correct the answer accordingly by shifting the coordinates in the solution. We can describe the circle with
$x^{2} + y^{2} = 4$
So that (for the upper-half semicircle)
$y = \sqrt{4 - x^{2}}$
Now, we find an equation for the line. We know that
$m = \frac{\Delta y}{\Delta x} = \frac{4}{2} = 2$
We also are given one point on the line: $(0,-2)$, so that the $y$-intercept is $-2$. Thus, the equation for the line is
$y = 2x - 2$
To find the intersection, we solve
$ \sqrt{4 - x^{2}} = 2x - 2$
which gives $x = \frac{8}{5}$, and plugging this into $y = 2x - 2$, we obtain $y = \frac{6}{5}$