Nach dem Essen räume ich die Tassen wieder in den Schrank ein.

Because nach is a preposition that takes the dative case.

• das Essen = the meal / the food (nominative or accusative)
• after nach, it becomes dem Essen (dative)

So:

• nach dem Essen = after the meal

This is something you usually just learn together with the preposition:

• nach + dative
• mit + dative
• für + accusative
• etc.

So the important pattern here is:

• nach dem Frühstück
• nach der Arbeit
• nach dem Essen

Because here Essen is being used as a noun, not as a verb.

In German, all nouns are capitalized.

Compare:

• essen = to eat (verb)
• das Essen = the meal / the food / eating (noun)

In nach dem Essen, it means after the meal or after eating, so it is treated as a noun and must be capitalized.

In a normal main clause, yes, German often looks like:

• Ich räume die Tassen ein.

But when another element comes first, German still keeps the finite verb in second position. This is the V2 rule.

Here, the sentence starts with Nach dem Essen, so the verb must come next:

• Nach dem Essen | räume | ich die Tassen wieder in den Schrank ein.

So the pattern is:

• Ich räume ... ein.
• Nach dem Essen räume ich ... ein.

This is very common in German:

• Heute gehe ich nach Hause.
• Am Abend koche ich.
• Nach dem Essen räume ich ... ein.

Because the verb is einräumen, which is a separable verb.

• einräumen = to put away / put back in / stow
• In a main clause, separable prefixes split off:
  • Ich räume die Tassen ein.

So in your sentence:

• räume = the main verb part
• ein = the separable prefix, sent to the end

Compare:

• Ich räume die Tassen ein.
• Nach dem Essen räume ich die Tassen wieder in den Schrank ein.

But in some other structures, the verb stays together:

• Ich möchte die Tassen in den Schrank einräumen.
• dass ich die Tassen in den Schrank einräume

So yes, ein at the end is completely normal for a separable verb in a main clause.

Here einräumen means something like:

• to put away
• to put back into a cupboard/cabinet
• to put in its proper place

So die Tassen in den Schrank einräumen is not just move the cups, but specifically put the cups away into the cupboard.

This is different from plain räumen, which often has a broader meaning related to clearing or tidying.

In everyday German, einräumen is very natural for putting dishes, groceries, clothes, etc. into the place where they belong.

Examples:

• Ich räume das Geschirr ein.
• Kannst du die Einkäufe einräumen?

Because this sentence describes movement into the cupboard, not location inside it.

German uses certain prepositions, including in, in two ways:

• accusative for direction / movement toward a destination
• dative for location / position

So:

• in den Schrank = into the cupboard (movement, destination)
• im Schrank = in the cupboard (location)

Compare:

• Ich stelle die Tassen in den Schrank. = I put the cups into the cupboard.
• Die Tassen stehen im Schrank. = The cups are in the cupboard.

That is why den Schrank is correct here.

Because Schrank is a masculine noun: der Schrank.

After in with movement/direction, German uses the accusative, and masculine accusative changes der to den.

So:

• nominative: der Schrank
• accusative: den Schrank

That gives:

• in den Schrank

If it were a different gender, the form would change differently:

• in die Tasche (feminine)
• in das Haus (neuter)
• in den Schrank (masculine)

Yes. Die Tassen is the direct object of the verb, so it is in the accusative case.

The noun is plural:

• singular: die Tasse = the cup
• plural: die Tassen = the cups

In German, the article die is used for:

• feminine singular nominative
• feminine singular accusative
• plural nominative
• plural accusative

So here die Tassen is plural accusative, but it looks the same as plural nominative.

That is normal in German.

Here wieder means again or, more naturally in English in this context, back.

So the sense is:

• I put the cups back in the cupboard

It suggests that the cups were taken out, used, and are now being returned to their usual place.

In this kind of household context, wieder often sounds very natural:

• Ich lege das Buch wieder auf den Tisch.
• Sie geht wieder nach Hause.
• Räum bitte alles wieder in den Schrank ein.

Yes, adverbs like wieder can sometimes move around, but their position can slightly affect emphasis.

In your sentence:

• Nach dem Essen räume ich die Tassen wieder in den Schrank ein.

This is a very natural placement. It connects well with the idea of putting the cups back where they belong.

You may also hear other word orders, but not every position sounds equally natural. German word order is flexible, but not random.

The sentence as given is a good standard model to learn:

• time phrase first
• finite verb second
• subject
• object
• adverb
• prepositional phrase
• separable prefix at the end

Yes. Schrank is a broad word.

Depending on context, it can mean:

• cupboard
• cabinet
• wardrobe
• closet

In this sentence, because we are talking about Tassen after a meal, cupboard or cabinet is the most natural translation.

So learners should not think that Schrank always has only one fixed English equivalent. The exact translation depends on what kind of thing is being stored.

That word order is possible in some contexts, but it sounds less neutral. It puts wieder later and can sound more marked or less natural to many learners’ ears.

The more standard, natural version is:

• Nach dem Essen räume ich die Tassen wieder in den Schrank ein.

That is the safest version to copy.

In German, adverb placement often depends on what you want to emphasize, but if you are unsure, the original sentence is a very good model.