"I thank her."
Translation:Ich danke ihr.
Well, maybe I can help. I saw on other commentaries here, a guy explaning that way: Here, it is used IHR because the verb DANKE requires dative cases, but why?
Well, there are four cases (as far as I know) in German: Nominative, Accusative, Dative, Genitive. Until this lesson, you might have seen Nominative and Accusative, but in this sentence, we have a Dative.
So, what's the difference between Accusative and Dative? Well, the way I understood is that Accusative cases is when somebody makes something towards something/somebody, like "Sie essen den Apfel". The man is eating (making something) the apple (towards the apple). The Dative cases, is when somebody/something RECEIVES something from another somebody, like this exercise "Ich danke ihr." You are thanking her for something, she is receiving your thanks.
Was it good? Hope I did not mixed it all up.
Estevao, great explanation. I normally think of the accusative as having a "direct" action on the object i.e. the subject is performing an action on a direct object (also known as transitive vs intransitive). This usually means that the verb requires a direct object, otherwise the sentence would sound awkward. "Sie essen" alone sounds funny: "You eat." You have to eat something in order for the sentence to be complete.
However, "sagen" "danken" "helfen" are all intransitive i.e. they do not require a direct object, nor do they have an effect on any object.
Schlagen - to hit - transitive Laufen- to walk - intransitive
That means "her (something that is feminine)", for example ihre Mutter = ""her mother". Using "her" as a possessive determiner uses a different word in German than "her" as a personal pronoun. Words often don't translate 1:1 between languages, especially when using them in different contexts.