Kannst du den Reißverschluss bitte kurz zumachen? Danach hänge ich den Mantel auf einen zweiten Kleiderbügel.

Kannst du ... ? is a very common way to make a polite request in German, literally Can you ... ?

So:

• Kannst du den Reißverschluss bitte kurz zumachen? = Can you quickly zip it up / close the zipper, please?

Grammatically, this is a yes/no question, so the finite verb comes first:

• Kannst = first
• du = second

Compare:

• Du kannst den Reißverschluss zumachen. = You can close the zipper.
• Kannst du den Reißverschluss zumachen? = Can you close the zipper?

Because Reißverschluss is the direct object of zumachen, so it takes the accusative case.

The noun is masculine:

• nominative: der Reißverschluss
• accusative: den Reißverschluss

So:

• Der Reißverschluss ist kaputt. = The zipper is broken.
• Ich mache den Reißverschluss zu. = I close the zipper.

That is why the sentence has den Reißverschluss.

Zumachen means to close, to shut, or in this context to zip up.

It is a very common everyday verb. With a zipper, it can sound more natural than a more formal verb like schließen.

Examples:

• die Tür zumachen = to shut the door
• das Fenster zumachen = to close the window
• den Reißverschluss zumachen = to close / zip up the zipper

So here it is an ordinary, natural spoken-German choice.

Because it follows the modal verb kannst.

Zumachen is a separable verb:

• base form: zumachen

When a separable verb is used as the main verb in a simple present tense sentence, the prefix separates:

• Ich mache den Reißverschluss zu.

But after a modal verb, the separable verb stays together as an infinitive at the end:

• Ich kann den Reißverschluss zumachen.
• Kannst du den Reißverschluss zumachen?

So:

• without modal: mache ... zu
• with modal: ... zumachen

Literally, kurz means short, but in this kind of request it often means something like:

• quickly
• for a moment
• just briefly

So bitte kurz softens the request and makes it sound casual and natural:

• Kannst du bitte kurz helfen? = Can you help for a second?
• Kannst du den Reißverschluss bitte kurz zumachen? = Can you quickly zip this up, please?

It does not mean the zipper will only be closed for a short time. It refers to the action being quick.

Danach means after that or afterwards.

German often puts time expressions first in the sentence. When that happens, the verb still has to stay in second position.

So:

• Danach hänge ich den Mantel auf einen zweiten Kleiderbügel.

Structure:

• Danach = first position
• hänge = second position
• ich = after the verb

If you started with ich, you would get:

• Ich hänge danach den Mantel auf einen zweiten Kleiderbügel.

That is also possible, but it gives a slightly different emphasis. Starting with Danach highlights the sequence of actions.

This is the normal verb-second rule in German main clauses.

In German main clauses, the finite verb must be in the second position. If something other than the subject comes first, the subject moves after the verb.

So:

• Ich hänge den Mantel auf einen zweiten Kleiderbügel.
• Danach hänge ich den Mantel auf einen zweiten Kleiderbügel.

This is a very important German word-order pattern.

More examples:

• Heute gehe ich nach Hause.
• Dann rufe ich dich an.
• Im Winter trage ich oft einen Mantel.

Here hänge means I hang or I will hang.

The verb is hängen. In this sentence it is being used transitively, meaning you are hanging something somewhere:

• Ich hänge den Mantel auf einen Kleiderbügel. = I hang the coat on a hanger.

Be careful: German distinguishes between:

• etwas hängen = to hang something
• etwas hängt = something is hanging

Examples:

• Ich hänge die Jacke an die Tür. = I hang the jacket on the door.
• Die Jacke hängt an der Tür. = The jacket is hanging on the door.

Because auf can take either accusative or dative, depending on whether there is movement/change of position or a fixed location.

Here, the coat is being moved onto the hanger, so German uses the accusative:

• auf einen zweiten Kleiderbügel = onto a second hanger

Compare:

• Ich hänge den Mantel auf einen Kleiderbügel.
  movement → accusative

• Der Mantel hängt auf einem Kleiderbügel.
  location → dative

So the sentence uses einen because it describes putting the coat onto the hanger.

Because zweiten is an adjective-like word modifying Kleiderbügel, and adjective endings change in German.

Here we have:

• auf einen zweiten Kleiderbügel

Since Kleiderbügel is masculine and the phrase is in the accusative singular with the article einen, the adjective takes -en:

• einen zweiten Kleiderbügel

This is the same pattern as:

• einen roten Mantel
• einen neuen Bügel
• einen langen Reißverschluss

Literally, zweiten means second.

In context, though, English will often translate it more naturally as a second or another:

• einen zweiten Kleiderbügel = a second coat hanger / another coat hanger

So the idea is that there is already one hanger, and the speaker will use an additional one.

Because that is simply the gender of the noun in German:

• der Kleiderbügel = the clothes hanger / coat hanger

So in the accusative singular it becomes:

• einen Kleiderbügel

Its plural is usually:

• die Kleiderbügel

As with many German nouns, the gender has to be learned together with the word.

Reißverschluss is a compound noun:

• reißen originally relates to pulling/tearing
• Verschluss = closure / fastening

Together, der Reißverschluss means zipper.

It is capitalized because all nouns in German are capitalized:

• der Reißverschluss
• der Mantel
• der Kleiderbügel

Also note the spelling ß in Reißverschluss. That letter is called Eszett or scharfes S.

Yes, in principle, but the tone changes a little.

• den Reißverschluss zumachen sounds very natural and everyday.
• den Reißverschluss schließen is also correct, but can sound slightly more formal or less conversational.

A native speaker would very often use zumachen in this kind of situation.

German often uses the present tense to talk about the near future when the meaning is clear from context.

So:

• Danach hänge ich den Mantel auf einen zweiten Kleiderbügel.

means:

• After that, I’ll hang the coat on a second hanger.

This is completely normal in German. You do not need werde ... hängen here.

Compare:

• Morgen gehe ich einkaufen. = I’m going shopping tomorrow.
• Danach hänge ich den Mantel auf einen zweiten Kleiderbügel. = After that, I’ll hang the coat on another hanger.