La ropa puede desteñir o encoger.

Because ropa is a collective/uncountable noun in Spanish. It means clothing / clothes in a general sense, but grammatically it behaves like a singular noun.

So Spanish says:

• La ropa puede...
• not normally Las ropas pueden... for everyday clothes

If you want a normal plural countable word, Spanish often uses las prendas instead.

Spanish often uses the definite article with nouns when speaking about things in general.

So:

• La ropa puede desteñir o encoger = Clothes can run or shrink / Clothing can run or shrink

English often drops the article in this kind of general statement, but Spanish usually keeps it.

Because the subject is la ropa, and ropa is singular.

• La ropa puede...
• Las prendas pueden...

Here puede means can / may in the sense of possibility, not permission.

So the sentence means that clothing may do these things when washed, not that it is allowed to do them.

Because after poder, Spanish uses the infinitive.

This works like English:

• can shrink
• can fade
• not can shrinks or can fades

So:

• puede desteñir
• puede encoger

That is the normal structure: poder + infinitive.

In a laundry context, desteñir means that the colour may run, bleed, or fade.

So if a red shirt destiñe, its dye may come out in the wash and affect other clothes, or it may lose some of its own colour.

That is why you often see desteñir in washing instructions and clothing warnings.

Here encoger means to shrink.

In other contexts, encoger can also mean to make something smaller or to draw something in, but with clothing and washing, the natural meaning is to shrink.

So La ropa puede encoger means the clothes may become smaller after washing or drying.

Yes, you could also say:

• La ropa puede desteñirse o encogerse

That is also natural Spanish.

In practice:

• desteñir / encoger without se is very common in short warnings and care instructions
• desteñirse / encogerse is also correct and can sound a bit more explicitly like undergo that change

So both versions are possible. The sentence you were given is short, natural, and very typical of label-style Spanish.

Usually, no—not in normal everyday Spanish when you simply mean clothes in general.

The most natural form is:

• la ropa

Las ropas does exist, but it is much less common and usually sounds more specific, literary, or unusual to learners expecting a simple everyday word for clothes.

If you need a plural countable alternative, use:

• las prendas

Roughly, in Spain:

• desteñir → des-te-NYEER
• encoger → en-ko-HER

A few key points:

• ñ sounds like ny in canyon
• the g in encoger before e sounds like the Spanish j: a throaty sound, stronger than English h
• both infinitives are stressed on the last syllable: desteñir, encoger

Because Spanish changes o to u only before words that begin with an o sound.

For example:

• uno u otro
• siete u ocho

But encoger begins with an e sound, so the conjunction stays o:

• desteñir o encoger

So the sentence is exactly as it should be.