Answer
$(4\pm\sqrt 7,2)$
Work Step by Step
Step 1. Given the circle with center at $(4,5)$ and radius $4$, we can write its equation as $(x-4)^2+(y-5)^2=16$
Step 2. To find the intersects, use $y=2$ in the equation above, we have $(x-4)^2+(2-5)^2=16\longrightarrow (x-4)^2=16-9=7$ which gives $x=4\pm\sqrt 7$
Step 3. The intersection points are $(4\pm\sqrt 7,2)$