What am I doing Wrong

4{ [ 5(z-4) +17] - [ 2(2z-3) +4 ] }

I found this answer 4z-20
but the correct answer is 4z-4

What did I do wrong?

Show your work if you want us to tell you WHAT you did wrong.

Here is the right way to do it; eliminating brackets from the inside out;
4{ [ 5(z-4) +17] - [ 2(2z-3) +4 ] }
4{ [ 5z - 20 +17] - [ 4z - 6 +4 ] }
4{ [ 5z - 3 ] - [ 4z - 2 ] }

I think that THIS is the step where you went wrong;
bracketing out the -(-) becomes a + you see

4{ [ 5z - 3 ] - 4z + 2 }
4{ z - 1 }
4z - 4

You probably did THIS;
4{ [ 5z - 3 ] - [ 4z - 2 ] }
4{ 5z - 3 - 4z - 2 }
4{ z - 5 }
4z - 20

4{ [ 5(z-4) +17 ] - [ 2(2z-3) +4 ] }
4 { [ 5z - 20 + 17] - [ 4z - 6 + 4] } <---i think you may have changed the -3 to a positive 3
4 { [ 5z - 3 ] - [ 4z - 2] }
4 { [ 5z -3 -4z +2 ] }
4 { z-1 }
4z-1

4{ [ 5(z-4) +17] - [ 2(2z-3) +4 ] }

4{ [ 5z - 20 +17] - [ 4z - 6 +4 ] }

4{ [ 5z - 3)] - [ 4z - 2 ] }

4(5z - 3 - 4z + 2)

4(z - 1)

4z - 4

:)

4{ [ 5(z-4) +17] - [ 2(2z-3) +4 ] } =
4{ [ 5z-20 +17] - [ 4z- 6 +4 ] } =
4{ [ 5z - 3] - [ 4z- 2] } =
4{ 5z - 3 - 4z + 2 } =
4{ z - 1 } =
4z - 4