Hey, I'm sorry if this is in the wrong place, I wasn't too sure where to put a transformation question. No idea what I'm doing wrong, thanks for taking the time to look over my problem!

The question I've got here;

is stretched horizontally by a factor of 2 about the line x = 4 What is the resulting equation?

I started by moving the graph to the left by 4 units to line up x=4 with the y-axis. Which is what a reference problem in my textbook is doing,

From here I stretched by a factor of 2 by replacing all with

Lastly, I moved the graph back by 4 units to the right, to place it back with the line about which it was being stretched.

I must be doing something wrong, as I don't see why the intermediate steps of translating it 4 units left and then back had anything to do with it.

The correct answer to this problem is

I have NO idea how they could manage to get this! Does anyone have any idea how I'm going wrong? Thanks in advance for any and all help!