Translation:La hundoj atendas ekster la domo.
Could someone please explain the structure of "ekstere de" as opposed to just "ekster"?
They're more or less the same.
The given translation does not use "de", and the English "of" sounds slightly odd to me. We might talk of something being "ON the outside of the house"., but in a sentence like the one here, we'd normally just say "outside the house".