[LumpTom]

Then hide red cube and select destination vertice (on white cube) where surfaces need to be moved, and again, fill its position to the "Move to" fields. See first image.

Then select desired surfacese to move (here it is bottom and front side of yellow cube) - see second image. Then in Hierarchy window unhide and select red cube with shift pressed (add red cube surfaces to selected surfaces of yellow cube). See third image.

Last step is move whole selections to destination with "Move to" button. It moves centre of red cube within yellow cube surfaces to the destination position. Important is, that all moved surfaces must be inside red cube. Then select red cube as object and delete it. Voila ... see fourth image :-)