If dual-case prepositions describe movement from one place to another, they are followed by the accusative case. Otherwise, they take the dative. Ich stecke die Schuhe unter das Bett.

The German word for 'car' is neuter and is the direct object of the sentence, so the accusative case is used. Das blaue T ... Sie hat der deutschen Lehrerin die Hausaufgaben gegeben.