Das war ganz einfach für ihn.
(That was quite easy for him.)
Why are we using the accusative case? I am also confused about what the subject, the object, and the indirect object are in this sentence.
I expected the dative, but still, I'm not so sure. I think the subject is whatever "Das" is referring to here. So, das is doing the action "war". The problem I have is that I don't see an object who is receiving the action, for it to be accusative.
Wajaap's answer sums it up pretty well, but some additional detail might help. A verb that describes the subject, or equates it with something else in some way is called copulative. An example is sein, and as such it's not transitive and so it does not have an (accusative) object. The basic form of the sentence, in this case, is "(subject) sein (adjective)." The subject is das and the adjective is einfach. The das here is a pronoun meaning "that" as in "that task", whatever it was that "he" was doing. The full sentence has some additional modifiers. First ganz modifies einfach changing "easy" to "quite easy". Second, the phrase für ihn, the preposition für followed by the accusative, modifies the sentence itself. The ihn is actually a prepositional object since it's governed by a preposition. The case of a prepositional object in German is determined by a couple of factors, but here it's easy since für is always used with the accusative case.
You should forget about the terms "direct object" and "indirect object" in German grammar; they may be useful for English grammar, but they can cause confusion when you try to apply them to German. Use "accusative object" and "dative object" instead. The problem is that German sometimes uses the dative whereas English used a direct object. For example helfen uses a dative object while "help" is a transitive verb in English that uses a direct object. For objects that are associated with a preposition rather than the verb itself, the term "prepositional object" may be useful. For nouns used with a copulative verb, the term "predicate object" seems most appropriate, and there are additional rules to predict the actual case of a predicate object. For example in Ich bin ein Narr, the predicate object is ein Narr in the nominative case. (The accusative case would be einen Narren and the dative case would be einem Narren.) The upshot is that while the terms "direct object" and "indirect object" may predict German cases some of the time, they often predict the wrong case and you're better off not trying to apply them to German.
We are using Accusative when we can make the question: for whom was it easy? For him. -> Für ihn. Anyways it is important for you to know that the preposition Für always goes with Accusative.
An other example:
-Es ist unmöglich für mich ein Auto zu kaufen.
(It is impossible for me to buy a car.)
