You can do this a few different ways. You can graph it on a graphing calculator and use the trace function to find the intercepts. If you don't have a calculator you can plug in points for y and then solve for x. You know that this is a parabola because of the x^2. There are going to be 2 x values because you will have to take the square root.
Let's take the example of setting y=0 which will also give us the x intercepts
Plug that in and solve for x
0=x^2-4
add 4 to both sides
4=x^2
take the square root of both sides
x=+2 and -2
so you have two points 0,2 and 0,-2
Now to find the y intercept you plug in 0 for x and solve for y
y=0^2-4
y=-4
you now have a 3rd point -4,0 which is the y intercept. You can draw the graph with that and see that the parabola is split by the y axis with a vertex at -4,0.
Here is the graph.