This is sure to be something simple, but when I push/pull the various sections of this shape, they do not form solids, with the exception of the bottom right hand section. Instead, they form boxes which are hollow when viewed from behind, I don’t understand why. I would like to pull the whole shape out by 120mm
Very likely you are starting with a surface that has been divided into smaller faces. What is happening is exactly the same as if you were trying to push a hole through as for a window.
When you pushpull a face that is inset into or touching another face, SketchUp assumes by default that you meant to pushpull an inset, so it deletes the starting face. To override this default, press ctrl (option on Mac) after you activate the pushpull tool.