Meine Mitbewohnerin hängt die Hemden lieber auf den Wäscheständer, weil der Trockner sie manchmal kleiner macht.

Because Mitbewohnerin is a feminine noun, meaning female roommate / flatmate.

• der Mitbewohner = male roommate
• die Mitbewohnerin = female roommate

Since it is feminine singular in the nominative case, the possessive changes to meine:

• mein Mitbewohner = my male roommate
• meine Mitbewohnerin = my female roommate

In this sentence, meine Mitbewohnerin is the subject, so nominative is used.

Die Hemden is the direct object of the verb aufhängen here: it is the thing being hung up.

So the structure is:

• Meine Mitbewohnerin = subject
• hängt ... auf = verb
• die Hemden = direct object

Because Hemden is plural, the article is die in both nominative and accusative plural, so the form does not change. That can be confusing for English speakers, but here the function is clear from the sentence structure.

Because the verb is aufhängen, which is a separable verb.

In a normal main clause, the conjugated part goes to the second position, and the prefix goes to the end:

• Sie hängt die Hemden auf.

So in your sentence:

• hängt = conjugated verb part
• auf = separable prefix at the end of the main clause

This is very common in German:

• anrufen → Ich rufe dich an.
• aufstehen → Er steht früh auf.

Because auf can take either the accusative or the dative, depending on the meaning.

Here, there is movement toward a destination: the shirts are being hung onto the drying rack. That is why German uses the accusative:

• auf den Wäscheständer

If the sentence described location without movement, you would use the dative:

• Die Hemden hängen auf dem Wäscheständer.
  = The shirts are hanging on the drying rack.

So the basic contrast is:

• wohin? where to? → accusative
• wo? where? → dative

Der Wäscheständer means clothes drying rack or laundry rack.

It is a compound noun:

• Wäsche = laundry
• Ständer = stand / rack

German often combines nouns into one long word. The last part usually determines the gender, so because der Ständer is masculine, the full word is also masculine:

• der Wäscheständer

Here, lieber means preferably / rather.

So:

• Sie hängt die Hemden lieber auf den Wäscheständer
  = She prefers to hang the shirts on the drying rack

It often expresses preference between options, sometimes without stating both options explicitly. In this sentence, the unstated alternative is using the dryer.

Related forms:

• gern = gladly / like doing
• lieber = rather / prefer
• am liebsten = most of all

For example:

• Ich trinke gern Tee. = I like drinking tea.
• Ich trinke lieber Tee als Kaffee. = I prefer tea to coffee.

Because weil introduces a subordinate clause, and in German subordinate clauses the conjugated verb usually goes to the end.

Main clause:

• Meine Mitbewohnerin hängt die Hemden lieber auf den Wäscheständer

Subordinate clause:

• weil der Trockner sie manchmal kleiner macht

So after weil, the normal English-like word order changes. That is why macht comes at the end.

This is a very important German pattern:

• Ich bleibe zu Hause, weil ich krank bin.
• Sie lernt Deutsch, weil sie in Berlin arbeitet.

Because der Trockner is the subject of the weil clause.

In weil der Trockner sie manchmal kleiner macht:

• der Trockner = subject
• sie = object
• macht = verb at the end

So the dryer is the thing doing the action: it makes them smaller.

If Trockner were the direct object, you would see den Trockner, but that is not the case here.

Here, sie refers to die Hemden.

That means:

• der Trockner sie manchmal kleiner macht
  = the dryer sometimes makes them smaller

This can be confusing because sie can mean several things in German, including:

• she
• they
• her
• them
• formal you in other contexts as Sie

Here, the meaning is them, because it refers back to die Hemden.

Kleiner macht means makes smaller. It uses:

• machen = to make
• kleiner = smaller

This is a common German way to express change:

• etwas größer machen = make something bigger
• etwas kleiner machen = make something smaller
• etwas sauber machen = make something clean / clean something

Using kleiner suggests that the shirts become smaller than they were before, which fits the idea of clothes shrinking in the dryer.

The main clause follows the usual German verb-second pattern.

The sentence begins with the subject:

• Meine Mitbewohnerin

Then comes the conjugated verb in second position:

• hängt

Then the other elements:

• die Hemden
• lieber
• auf den Wäscheständer

And finally the subordinate clause:

• weil der Trockner sie manchmal kleiner macht

So the rough structure is:

• Subject + verb + other information + subordinate clause

A useful thing to remember is that even though aufhängen is the full verb, only the conjugated part hängt stays in second position; the prefix auf moves later in the clause.