We're given a parabola
[tex] y=x^2-4[/tex]
and a line
[tex]y = 2x+b[/tex]
The zeros of the parabola are
[tex]0=x^2-4[/tex]
[tex]4=x^2[/tex]
[tex]x=\pm 2[/tex]
We see that (-2,0) is on the line as well:
[tex]y = 2x+b[/tex]
[tex]0 = 2(-2)+b[/tex]
[tex]b=4[/tex]
Choice D