How best to build this wall out

[champy]

What's the best way to build the wall on the right out 20cm so that its inline with the perpendicular wall at the back. I'd like to then hang a door, sealing off the space on the right.

you can see the difference with the gap in the floor.

 

[^woody^]

Timber stud

 

[champy]

Timber stud

Should I make an actual stud partition, or just screw 3 timbers side by side?

With a stud partition the noggins would only be a few cm across

 

[^woody^]

200mm is 2x 4x2 and then a top and sole plate and a noggin or two. You won't do it with just three timbers without messing about trying to pack one of them out.

A sole and top plate will allow you to secure the top and bottom too.