"We like the apple."
Translation:Wir mögen den Apfel.
Der Akkusativ is the case used for the thing being acted upon.
Basic grammar: a sentence (ein Satz) must have, at a minimum, a subject and a verb. Zum Beispiel:
- Der Junge isst. == The boy eats. Hier ist "der Junge" das Subjekt und "isst" das Verb. The boy is the actor and the action he is taken is described by the verb.
If the boy eats something, perhaps an apple, then we have: "Der Junge isst einen Apfel." The apple is the thing being acted upon: it is being eaten. Das ist ein "direkt Objekt", und der Fall ist "Akkusativ". Similarly, der Junge wirft den Ball. The ball is being thrown, and the boy is the one throwing it.
Ania does a great job of explaining die Fälle in this series of videos.
"Das" is for neuter names, while Apfel is a masculine name, so the article is "der", which becomes "den" in the accusative.
I think that'd be "wir haben gern . . . ," which would literally be "we like having . . . ." That seems to be the same.