После стирки я повесил полотенце на верёвку на балконе.

Because после requires the genitive case.

• Dictionary form: стирка
• After после: стирки

So:

• после стирки = after washing / after the laundry

This is a very common pattern in Russian:

• после работы = after work
• после урока = after the lesson
• после дождя = after the rain

Стирка means washing clothes / doing the laundry / a wash.

In this sentence, it refers to the towel having been washed. English can say after washing, but Russian often uses a noun here:

• после стирки = literally after the washing / after laundry

It sounds natural and compact in Russian. If you wanted a more explicit version, you could say something like:

• После того как я постирал полотенце... = After I washed the towel...

But после стирки is shorter and very natural.

Повесил is the past tense, masculine singular form of повесить.

That tells you two things:

1. The action is in the past
2. The speaker is understood to be male

So:

• я повесил = I hung
• я повесила = I hung (if the speaker is female)

Also, повесить is a perfective verb, so повесил presents the action as completed: the towel was successfully hung up.

Compare:

• я повесил полотенце = I hung up the towel / I got it hung
• я вешал полотенце = I was hanging the towel / I used to hang the towel / I hung the towel repeatedly

In this sentence, the completed action is what matters, so повесил is the natural choice.

Because полотенце is the direct object of the verb повесил, and for an inanimate neuter noun, the accusative singular looks the same as the nominative singular.

So:

• nominative: полотенце
• accusative: полотенце

That is why the word does not visibly change.

Compare with a feminine noun:

• книга → книгу in the accusative

But with полотенце, the form stays the same.

This is a very important Russian pattern.

The preposition на can mean different things depending on whether you are talking about:

• movement toward a destination → usually accusative
• location → usually prepositional

In this sentence:

• на верёвку = onto the clothesline
  This is a destination, so it uses the accusative: верёвку

• на балконе = on the balcony
  This is a location, so it uses the prepositional: балконе

So the structure is:

• повесил на верёвку = hung onto the line
• на балконе = located on the balcony

This same contrast appears in many Russian phrases:

• положить на стол = put onto the table
• лежать на столе = lie on the table

Literally, верёвка means rope or cord. In this context, it naturally means a clothesline.

So на верёвку here is understood as:

• onto the line
• onto the clothesline

If you wanted to be more explicit, Russian can say:

• бельевая верёвка = clothesline

But in everyday speech, just верёвка is often enough when the context is laundry.

A little, but in normal context it is easy to understand.

The sentence is:

• ...повесил полотенце на верёвку на балконе

This is understood as:

• I hung the towel on the clothesline on the balcony

The second phrase, на балконе, tells you the location of the action or of the clothesline. Russian allows this kind of stacking of prepositional phrases quite naturally.

If you wanted to make it more explicit, you could say:

• После стирки я повесил полотенце на балконе на верёвку.
• После стирки я повесил полотенце на верёвку, которая была на балконе.

But the original sentence sounds normal.

Yes. Russian often omits subject pronouns when they are clear from the verb form or the context.

So you could say:

• После стирки повесил полотенце на верёвку на балконе.

That can still mean After washing, I hung the towel on the clothesline on the balcony, especially in conversation where the subject is already understood.

However, я is perfectly fine here. Including it can:

• make the subject explicit
• sound slightly more neutral or clearer
• add a little emphasis to I

Yes, Russian word order is flexible.

The original sentence starts with:

• После стирки = After washing

Putting that first sets the time frame right away. This is very natural.

Other possible orders include:

• Я после стирки повесил полотенце на верёвку на балконе.
• Полотенце я повесил на верёвку на балконе после стирки.

These are grammatically possible, but the emphasis changes.

The original order is natural because it goes:

1. when it happened
2. who did it
3. what they did
4. where they hung it

Yes, absolutely.

That would give you a full clause:

• После того как я постирал полотенце, я повесил его на верёвку на балконе.

This means:

• After I washed the towel, I hung it on the clothesline on the balcony.

Difference in style:

• после стирки = shorter, more compact, more noun-based
• после того как я постирал полотенце = more explicit, more clause-based

Russian often prefers compact noun phrases like после стирки when the meaning is obvious.

Because стирать is the normal verb for washing clothes, laundry, fabric items.

A towel is typically something you launder, so Russian uses the vocabulary of laundry:

• стирать полотенце = wash/launder a towel
• стирка = washing laundry / laundry

Мыть is more for washing hard surfaces, body parts, dishes, and similar things:

• мыть руки = wash hands
• мыть посуду = wash dishes
• мыть пол = wash the floor

So with полотенце, стирка is the most natural choice.

Usually, yes.

In the context of после стирки and на верёвку, the natural interpretation is:

• the towel was hung up to dry

Russian does not need to say that explicitly here, because the situation already makes it clear. English often works the same way:

• I hung the towel on the line naturally suggests drying

If you wanted to be fully explicit in Russian, you could say:

• повесил полотенце сушиться = hung the towel up to dry

But in this sentence, that extra wording is unnecessary.

The standard stresses are:

• по́сле
• сти́рки
• пове́сил
• полоте́нце
• на
• верёвку
• на
• балко́не

So a rough stress guide is:

• По́сле сти́рки я пове́сил полоте́нце на верёвку на балко́не.

A few of these are especially worth memorizing because learners often misplace the stress:

• пове́сил
• полоте́нце
• верёвка / верёвку
• балко́н / на балко́не