How would you solve this? (subcrating solids)

[Rhasdra]

Hi hi!

I've been wrapping my head around for the last 2 hours or so on drawing solids interacting, in this case, subtracting one solid of another.

I've made a 3d model of what I'm trying to do, and I'd like to know how would you guys solve this in 2d drawing.
I just can't figure a way of drawing this when none of the vertical or horizontal axis are parallel.

Link for images of the 3d model >
http://imgur.com/a/z1hJP

[BrushNoir]

Maybe this can help you http://drawabox.com/lesson/2

[Rhasdra]

Thank you so much guys!
Yeap, it seems a intuitive approach is much more viable.
Thinking in the planes individually really helps, and I came across some methods on how to find those distorted forms kind of intuitively, here's one of them:

https://www.youtube.com/watch?v=Wr0SXRrzch8


Thank you so much for the help, I'm so happy I learned how to solve this hahaha