Эта ткань сильно мнётся, если положить её в сумку.

Because эта has to agree with ткань in gender, number, and case.

• ткань is feminine
• singular
• nominative here, because it is the subject of the sentence

So this fabric = эта ткань.

Compare:

• этот стол = this table
• эта ткань = this fabric
• это платье = this dress
• эти вещи = these things

Because ткань is the thing being described — the subject of the sentence.

The sentence is about what the fabric does:

• Эта ткань сильно мнётся = This fabric wrinkles a lot / gets very creased

So ткань stays in the nominative, which is the normal case for the subject.

Literally, сильно often means strongly, but in this sentence it is more natural in English as:

• a lot
• badly
• easily, depending on context

So сильно мнётся does not mean the fabric is wrinkling in a physically strong way. It means it wrinkles quite badly / very easily / a lot.

A natural translation would be:

• This fabric wrinkles badly if you put it in a bag.
• This fabric creases very easily if you put it in a bag.

Мнётся comes from the verb мяться, which means:

• to get wrinkled
• to get creased
• to crumple easily

So ткань мнётся means something like:

• the fabric wrinkles
• the fabric gets creased
• the fabric crumples easily

In English, we often use either:

• an active-style wording: This fabric wrinkles easily
• or a passive-like wording: This fabric gets wrinkled easily

Russian uses мяться very naturally here.

The -ся makes the verb reflexive, but reflexive verbs in Russian are not always literally reflexive in the English sense.

Here, мяться does not mean the fabric is wrinkling itself. Instead, the reflexive form gives a meaning like:

• to become wrinkled
• to get creased

So:

• мять = to crumple / wrinkle something
• мяться = to get crumpled / to wrinkle

This is a very common Russian pattern:

• открывать = to open something
• открываться = to open / to be opened
• ломать = to break something
• ломаться = to break / to get broken
• мять = to wrinkle something
• мяться = to wrinkle / get wrinkled

This is about aspect and also about the kind of structure being used.

Положить is perfective, meaning a single completed action: to put.

Here the sentence means:

• if you put it in a bag
• when it is put in a bag

That situation is viewed as one complete action, so положить fits well.

Why not класть?

• класть is imperfective
• it suggests an ongoing, repeated, or process-like action
• that is less natural here

Why not если положишь?

• You certainly could say that in a more direct sentence:
  Эта ткань сильно мнётся, если положишь её в сумку.
• But если положить... is a more general, impersonal way of saying if one puts it / if you put it

So если положить её в сумку is a common Russian way to express a general condition.

Russian often omits the subject in this kind of general statement.

So если положить её в сумку means something like:

• if you put it in a bag
• if one puts it in a bag
• if it is put in a bag

The subject is intentionally generic. It does not refer to a specific person.

This is a very natural Russian pattern when making general observations:

• Если добавить сахар, будет слаще.
  If you add sugar, it will be sweeter.
• Если поставить цветы в воду, они дольше стоят.
  If you put flowers in water, they last longer.

English usually inserts you, but Russian often does not need to.

Because её is the accusative form of она.

Here, the fabric is the direct object of положить:

• положить её = to put it

So:

• она = she / it, as the subject
• её = her / it, as the object

Since ткань is feminine, the pronoun used for it is the feminine form.

Because в can take either the accusative or the prepositional, depending on meaning.

Here there is movement into the bag:

• положить её в сумку = to put it into a bag

Movement toward/into something takes the accusative:

• в сумку
• в коробку
• в шкаф

Compare that with location:

• в сумке = in the bag
• в коробке = in the box
• в шкафу = in the wardrobe/cabinet

So:

• в сумку = into the bag
• в сумке = in the bag

Because если положить её в сумку is a subordinate clause, and Russian normally separates subordinate clauses with a comma.

So:

• Эта ткань сильно мнётся, если положить её в сумку.

This is similar to English, where we often separate clauses too, though punctuation rules are not always identical.

Сумка usually means a bag of the everyday carrying kind:

• handbag
• shoulder bag
• tote bag
• general bag

In this sentence, в сумку is naturally understood as in a bag.

If Russian wanted to be more specific, it could use other words:

• пакет = plastic bag, shopping bag
• рюкзак = backpack
• чемодан = suitcase

So сумка here is a normal, fairly broad word for bag.

It is in the present tense, but the meaning is really a general truth / characteristic.

• мнётся is present tense
• but the sentence is not about something happening right now only

It means:

• This fabric tends to wrinkle a lot if you put it in a bag
• This fabric wrinkles easily in that situation

Russian present tense is often used this way for general properties:

• Этот материал быстро сохнет. = This material dries quickly.
• Шерсть колется. = Wool feels itchy/prickly.
• Бумага легко рвётся. = Paper tears easily.

Yes. Russian word order is flexible, though the original order is very natural.

Original:

• Эта ткань сильно мнётся, если положить её в сумку.

You could also hear:

• Если положить её в сумку, эта ткань сильно мнётся.

That puts more focus on the condition first: if you put it in a bag.

Russian word order often changes for:

• emphasis
• style
• information structure

But the basic meaning stays the same.