"Where do you hide the breadboard in this house?"
Translation:Hvor gemmer I skærebrættet her i huset?
I see now what you mean. I am not a native speaker of Danish but it seems that your assumption is right. If you do a Google search for "her i huset" (including the quotes) you get many hits. "Her i" seems to be a common expression. As far as I know the words "denne" and "dette" are mainly used in written language, while in spoken language the expressions "den her" and "det her" are used. So "her i" can actually mean "in this", while "der i" can mean "in that". For me as a native German, "her i huset" literally translates to "hier im Haus", which is also very common in German and which is equivalent to "in this house".