Translation:When they came home, the dog had died.
Ok. I keep getting dinged for the order of "noun/pronoun - verb" in the second half of a sentence.
In this case, it's "hadde hunden." In the previous sentence (which I also just got dinged for - "Det koster mye mer enn hva vi hadde trodd."), it's "vi hadde."
How can I tell which goes first in instances like these where each sentence has an introductory portion? Is it merely the presence of a comma?
The difference between "Da de kom hjem, hadde hunden dødd" and "Det koster mye mer enn hva vi hadde trodd" is that the second part of the second sentence starts with a question word 'hva'. Inversion of the subject and verb leads to a question. So rather than saying "It costs more than what we had thought" your translation said "It costs more than what had we thought?"
When a subordinate clause is fronted in a sentence I think a comma is required before the verb of the main clause. So, that could be a clue to use when translating from the written word.