Мама прикрепила простыню к верёвке деревянной прищепкой.

Because it is the direct object of the verb прикрепила — it is the thing that got attached.

For most feminine nouns ending in -а or -я, the singular accusative changes as follows:

• -а → -у
• -я → -ю

So:

• простыня = nominative singular
• простыню = accusative singular

That is why Russian says прикрепила простыню.

The preposition к normally requires the dative case and means to, toward.

So:

• верёвка = rope, clothesline
• к верёвке = to the rope / to the line

This is a very common pattern:

• к столу = to the table
• к двери = to the door
• к верёвке = to the rope

Because it is in the instrumental case, which here shows the tool or means used to do the action.

So the sentence means that she attached the sheet using a clothespin.

• прищепка = clothespin
• прищепкой = with a clothespin / by means of a clothespin

Russian often uses the instrumental without a preposition to express the instrument:

• писать ручкой = to write with a pen
• резать ножом = to cut with a knife
• прикрепить прищепкой = to attach with a clothespin

Because Russian often uses the bare instrumental case to mean with, using.

So прищепкой already carries the idea of with a clothespin.

If you say с прищепкой, that usually sounds more like together with a clothespin rather than by means of a clothespin. In this sentence, the instrumental without a preposition is the natural choice.

It agrees with прищепкой.

Both words are:

• feminine
• singular
• instrumental

So:

• деревянной прищепкой = with a wooden clothespin

The adjective matches the noun it describes in gender, number, and case.

In the past tense, Russian verbs agree with the subject in gender and number.

The subject is мама, which is feminine, so the past-tense verb takes the feminine ending -ла:

• прикрепил = he attached
• прикрепила = she attached
• прикрепило = it attached
• прикрепили = they attached

So Мама прикрепила means Mom attached.

Because прикрепила is perfective, and it presents the action as a completed whole: she attached it successfully.

Compare:

• прикрепила = attached, fastened, completed the action
• прикрепляла = was attaching / used to attach / attached repeatedly or as a process

In a single finished event like this, perfective прикрепила is the natural choice.

Here is the breakdown:

• Мама — nominative
  The subject: the person doing the action.

• простыню — accusative
  The direct object: the thing being attached.

• к верёвке — dative
  Used after к.

• деревянной прищепкой — instrumental
  The means/tool used.

This sentence is a good example of how Russian uses case endings instead of English-style word order or prepositions alone.

Yes. Russian word order is more flexible than English because the case endings show the grammatical roles.

This sentence is perfectly natural, but other orders are also possible, for example:

• Мама прикрепила простыню к верёвке деревянной прищепкой.
• Мама деревянной прищепкой прикрепила простыню к верёвке.
• Простыню мама прикрепила к верёвке деревянной прищепкой.

The basic meaning stays the same, but the focus or emphasis can shift.

English relies much more on fixed word order; Russian relies much more on endings.

Because Russian has no articles.

So:

• мама can mean mom, the mom, or a mom
• простыню can mean the sheet or a sheet
• прищепкой can mean with a clothespin or with the clothespin

Russian usually leaves this to the context.

Yes. The dictionary form is верёвка, with ё.

So in this sentence:

• верёвка
• к верёвке

In many printed texts, Russian writers replace ё with е, so you may also see веревка and к веревке. But the pronunciation still has the yo sound.

A helpful stress-marked version is:

Ма́ма прикрепи́ла простыню́ к верёвке деревя́нной прище́пкой.

Approximate pronunciation:

• Ма́ма = MAH-ma
• прикрепи́ла = pree-kree-PEE-la
• простыню́ = pruh-stih-NYU
• к верёвке = k vee-RYOV-kye
• деревя́нной = dee-ree-VYAN-nuy
• прище́пкой = pree-SHYEP-kuy

For learners, the most important stress points here are:

• прикрепи́ла
• простыню́
• верёвке
• деревя́нной
• прище́пкой

Literally, yes: верёвка means rope or cord.

But in everyday context, it can also refer to a clothesline. So in this sentence, English might naturally translate it as clothesline, even though the Russian word itself is rope/line.

That is very normal in Russian household vocabulary.