I really have no idea what that means or how it happened accidentally? You can still edit that reply and remove the link to your web site and the image of your business card.
When you post a screen shot of code/geometry like you did, it’s reasonable to assume you have a file and could post something more useful than an image. It really saves so much time and makes it easier to offer help. I didn’t post my code file because you didn’t post yours. See what I mean?
I added very little to @anikolo’s code and my screen image is clear enough to reproduce it, isn’t it? I extruded the Boundary surface down ("-x" expression on Extr ‘D’ input) to create a solid, moved the spheres up (‘Z’ vector) by a fraction of their respective radii (‘height’ slider), and then subtracted them (SDiff) from the extrusion solid. Simple.
As to how to handle spheres that cross the boundary edges, you can ignore that detail as I did, or you can cull spheres that cross the edges before doing the SDiff, or you can reduce the radii to not exceed the distance to the nearest edge using Crv CP (Curve Closest Point).