I need help on this problem how do you solve this absolute value?

When solving an absolute value problem, I would isolate the absolute value until you get a form like

|z| = some number

In this case this would invole subtracting 4 from both sides

|z| + 4 - 4 = 9 - 4 ==> |z| = 5

Now that we are here you have to remember that the absolute value is both the positive and negative value. So:

|z| = 5 ==> z = 5 and z = -5