Learn Russian: Он заплатил аванс за два дня до поездки. - He paid the advance two days before the trip.

In Russian, to say how much time elapsed before an event, you use the structure за + [amount of time in Accusative] + до + [the event in Genitive]. You cannot just literally translate 'two days before'; without за, the phrase два дня до поездки would mean 'two days until the trip' (like the subject of a sentence), rather than acting as a time marker telling us exactly when he paid.

The lesson says the amount of time is in the Accusative case. Why is it два дня?

Два дня is actually the Accusative form here. Because 'days' are inanimate, the Accusative of the number two looks exactly the same as the Nominative. As a quick refresher on numbers, два requires the noun that follows it to be in the Genitive singular, which is why день becomes дня.

What case is поездки, and why?

It is in the Genitive case. The preposition до (meaning 'before' or 'until') always requires the Genitive. The dictionary form is поездка (a trip), and since it is a feminine noun ending in -а, the ending changes to -и in the Genitive.

Why didn't the direct object аванс change its ending?

Аванс (an advance payment or deposit) is the direct object of the verb заплатил, so it is indeed in the Accusative case. However, because it is a masculine, inanimate noun ending in a consonant, its Accusative form is identical to its dictionary (Nominative) form.