"The government promotes the project."
Translation:Die Regierung fördert das Projekt.
As an online dictionary could tell you, it's das Projekt.
I'm not quite sure what you mean though - when I hover over the article before Projekt (which is das) I see hints for "the", "this" and "that". Hovering over Projekt itself confirms that the gender is neuter. If you meant you hovered over the word "the" in the English sentence, then you should expect to see any of der/die/das/den/dem/etc. suggested. It's not a peek at the answer - but rather connected to the database of all possible meanings, which may or may not be applicable to the answer.
If you had some other kind of strange behaviour, you could post a screenshot to clarify.