Consider each of the options.
A is incorrect, as for [tex]x=2[/tex], [tex]y=2[/tex], while the equation suggests that [tex]y=|x|-4 = -2[/tex].
B is incorrect, as for [tex]x=2[/tex], [tex]y=2[/tex], but the equation suggests that [tex]y=|x+4| = 6[/tex].
C is incorrect, as once again, [tex]x=2[/tex], [tex]y=2[/tex], but the equation suggests that [tex]y=|x|+4 = 6[/tex].
D, on the other hand, satisfies all of the given datapoints, so it is the correct answer.
