Das Bett des Hundes war leer. The neuter noun 'bed' belongs to the 'dog', which is a masculine noun in German. We must use the genitive case here to show the possession. Sie hat der deutschen ...

Otherwise, they take the dative. Ich stecke die Schuhe unter das Bett. – I put the shoes under the bed. Die Schuhe sind unter dem Bett. – The shoes are under the bed. In the first sentence ...