I'm not sure I follow all of this.

Parts seem hazy, especially dollars being continuous.

Here's what I get...

on (0,23)

Next you have Y given X as uniform on 2X....

So

where we have 0<x<23 and 0<y<2x

which I would rewrite as either 0<y<2x<46 or 0<y/2<x<23

IS this what you're looking for?

I can get the density of Z=Y-X if you wish, but I would only do that if this makes any sense to you.