Τον Ιούνιο και τον Ιούλιο η φίλη μου προτιμάει φούστες και κοντομάνικες μπλούζες.

Because Greek often uses the accusative for time expressions like months.

• ο Ιούνιος = June

• τον Ιούνιο = in June / during June

• ο Ιούλιος = July
• τον Ιούλιο = in July / during July

So in this sentence, τον Ιούνιο και τον Ιούλιο means in June and July.

Because each month has its own article, and repeating it is the normal, clear Greek way:

• τον Ιούνιο και τον Ιούλιο

This is more natural and complete than trying to use one article for both nouns.

Greek word order is more flexible than English word order.

Putting τον Ιούνιο και τον Ιούλιο first sets the time frame right away, something like:

• As for June and July, my friend prefers...

You could also say:

• Η φίλη μου προτιμάει φούστες και κοντομάνικες μπλούζες τον Ιούνιο και τον Ιούλιο

but the original order sounds very natural.

η φίλη μου means my friend, but specifically a female friend, because φίλη is feminine.

A few useful points:

• ο φίλος μου = my male friend
• η φίλη μου = my female friend

Depending on context, η φίλη μου can sometimes also mean my girlfriend, just as ο φίλος μου can sometimes mean my boyfriend. Context tells you which meaning is intended.

Also, Greek normally keeps the article:

• η φίλη μου = literally the friend my, but naturally my friend

Greek usually uses the definite article with possessed nouns:

• η φίλη μου = my friend
• το σπίτι μου = my house
• ο αδερφός μου = my brother

So the article is not extra here; it is the normal Greek pattern.

Both are correct.

• προτιμάει
• προτιμά

They both mean he/she prefers.

προτιμάει is very common in everyday speech and informal writing.
προτιμά is also standard and is often felt to be a bit shorter or slightly more formal.

So this sentence could also be:

• Η φίλη μου προτιμά φούστες και κοντομάνικες μπλούζες.

Because the sentence is talking about these clothes in general, not about a specific set of skirts and blouses.

So:

• προτιμάει φούστες = she prefers skirts
• προτιμάει κοντομάνικες μπλούζες = she prefers short-sleeved blouses

If you added articles:

• προτιμάει τις φούστες και τις κοντομάνικες μπλούζες

that would sound more like the skirts and the short-sleeved blouses, possibly referring to particular ones.

They are in the accusative plural, because they are the direct objects of προτιμάει.

• She prefers what?
  φούστες and κοντομάνικες μπλούζες

A useful thing to know is that for many feminine plural nouns in Greek, the nominative plural and accusative plural look the same.

So:

• φούστες can be nominative plural or accusative plural
• μπλούζες can also be nominative plural or accusative plural

And κοντομάνικες matches μπλούζες in gender, number, and case.

It means short-sleeved.

It is built from parts meaning:

• κοντό- = short
• μάνικο = sleeve

So κοντομάνικες μπλούζες means short-sleeved blouses/shirts.

Here κοντομάνικες is a feminine plural form because it describes μπλούζες, which is feminine plural.

Yes, Greek adjectives can often come either before or after the noun.

So you may see:

• κοντομάνικες μπλούζες

and also, in some contexts:

• μπλούζες κοντομάνικες

But the first version is more natural and neutral here. It sounds like the ordinary way to say short-sleeved blouses.

By itself, it most naturally sounds like a general habit:

• In June and July, my friend prefers skirts and short-sleeved blouses.

But context can make it refer to a specific year too. Greek, like English, often leaves that to the surrounding conversation.

Usually, in standard Greek, months are written with lowercase letters unless they begin a sentence:

• τον Ιούνιο και τον Ιούλιο is often seen
• but strictly standard style usually prefers τον Ιούνιο και τον Ιούλιο? Actually the important rule is that month names are generally not capitalized in Greek the way they are in English.

So many learners notice capitals because teaching materials often imitate English habits, but standard Greek normally writes month names in lowercase.

Roughly:

• Ιούνιο ≈ EE-oo-nee-o
• Ιούλιο ≈ EE-oo-lee-o

The stress is on ού in both words.

So:

• Ιούνιο → stress on ού
• Ιούλιο → stress on ού

Listening practice helps a lot here, because the vowel sequence at the beginning can feel unusual to English speakers.