Nach der Präposition wegen höre ich in diesem Satz den Genitiv, nicht den Dativ.

Because nach takes the dative here.

• Präposition is a feminine noun.
• Feminine singular in the dative is der.

So:

• nominative: die Präposition
• dative: der Präposition

That is why the sentence says nach der Präposition wegen.

Here nach means after.

So nach der Präposition wegen means after the preposition wegen.

This is not the nach meaning to or toward. It is the time/order meaning: something comes after something else.

Because in this sentence, wegen is being talked about as a word, not actually used in a normal phrase.

In other words, the sentence is meta-language: it is talking about grammar.

So wegen here means something like:

• the word wegen
• the preposition wegen

That is why it stands alone.

Yes, they are names of cases, but in this sentence they are also nouns and they function as the direct objects of höre.

The verb hören normally takes the accusative, so we get:

• ich höre den Genitiv
• ich höre den Dativ

Even though the words mean grammatical cases, their form in the sentence is determined by their grammatical role here, not by their meaning.

Because the sentence begins with another element: Nach der Präposition wegen.

In a German main clause, the finite verb must be in second position.

So the structure is:

1. Nach der Präposition wegen
2. höre
3. ich
4. the rest

If the sentence started with ich, then it would be:

• Ich höre in diesem Satz den Genitiv, nicht den Dativ.

But once the first phrase is moved to the front, the verb comes before the subject:

• Nach der Präposition wegen höre ich ...

Because in here expresses location, not movement.

The meaning is in this sentence, meaning inside this sentence / in the wording of this sentence. That is a static location, so German uses the dative.

• der Satz = masculine
• dative singular = diesem Satz

Compare:

• in diesem Satz = in this sentence, inside it, as location
• in diesen Satz = into this sentence, as movement

Here we need the first one.

Because in German, all nouns are capitalized.

The names of grammatical cases are nouns, so they are written with capital letters:

• der Genitiv
• der Dativ
• der Nominativ
• der Akkusativ

The same applies to Präposition and Satz.

This is a contrast:

• den Genitiv
• nicht den Dativ

The speaker is saying that the form they hear after wegen is genitive, not dative.

Placing nicht before den Dativ makes the contrast very clear. It negates that noun phrase specifically.

A similar English pattern would be:

• the genitive, not the dative

In standard German, wegen is traditionally followed by the genitive.

Examples:

• wegen des Wetters
• wegen der Krankheit

However, in everyday spoken German, many native speakers also use the dative, especially in some regions:

• wegen dem Wetter

So the sentence is pointing out that in this particular case, the speaker hears genitive, not dative.

A good rule for learners is:

• use genitive after wegen in careful standard German
• be aware that dative is common in speech

It does not mean that the speaker literally hears the word Genitiv.

It means the speaker hears a genitive form after wegen in the sentence being discussed.

So den Genitiv hören here means something like:

• to hear a genitive ending
• to hear a genitive noun phrase
• to notice that genitive is being used

This is a common kind of shorthand when talking about grammar.

Yes. A more neutral word order would be:

• Ich höre nach der Präposition wegen in diesem Satz den Genitiv, nicht den Dativ.

Or even more naturally in many contexts:

• Ich höre in diesem Satz nach der Präposition wegen den Genitiv, nicht den Dativ.

But German often moves a phrase to the front for emphasis or structure. In your sentence, Nach der Präposition wegen is placed first because that is the topic the speaker wants to highlight.