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 $y = \frac{6}{5}$