Learn Hardcore Croatian: Njegove čarape imaju mrlju koju ne mogu oprati bez dobrog deterdženta. - His socks have a stain that I can’t wash out without good detergent.

Njegove is the possessive adjective njegov (his) in the feminine plural nominative form, because it has to agree with the noun čarape.

čarapa = one sock (feminine singular)
čarape = socks (feminine plural, nominative)

So you need:

njegova čarapa (his sock – fem. singular)
njegove čarape (his socks – fem. plural)

Using njegova čarape would be ungrammatical because njegova is singular but čarape is plural.

Why is čarape in this form and not čarapa or čarapama?

Čarape is in the nominative plural, because it is the subject of the sentence:

Njegove čarape (His socks) – subject
imaju (have) – verb
mrlju (a stain) – direct object

Other forms:

čarapa – nominative singular (one sock)
čarapama – dative/locative/instrumental plural (to/at/with socks, etc.)

Here we are simply talking about his socks as the thing that has the stain, so we use nominative plural: čarape.

Why is it imaju and not ima?

The verb imati (to have) must agree with the subject in number:

On ima čarape. – He has socks. (ima = 3rd person singular)
Njegove čarape imaju mrlju. – His socks have a stain.
Here, the subject is čarape (plural), so the verb must be imaju (3rd person plural).

So:

singular subject → ima
plural subject → imaju

Why is mrlju used instead of mrlja?

Mrlju is the accusative singular form of mrlja (stain). In this sentence, mrlju is the direct object of the verb imaju:

Što imaju? (What do they have?) → mrlju (a stain)

For a feminine noun ending in -a, the accusative singular usually changes -a → -u:

nominative: mrlja (subject)
accusative: mrlju (direct object)

So mrlja would be correct if it were the subject, but here it is the object, so we need mrlju.

What does koju refer to, and why is that form used?

Koju is a relative pronoun (from koji) that refers back to mrlju.

Antecedent: mrlju (feminine, singular, accusative)
Relative pronoun: koju (feminine, singular, accusative)

Inside the relative clause koju ne mogu oprati, the pronoun is also the direct object of oprati:

(Ne mogu oprati) što? → koju (meaning mrlju)

Because mrlju is feminine singular, and it’s in the accusative, the pronoun must match: koju (fem. sg. acc.).

Why is it ne mogu oprati and not ne mogu prati?

Both oprati and prati come from the verb prati (to wash), but they differ in aspect:

prati – imperfective: the process of washing (to be washing, to wash in general)
oprati – perfective: to wash something completely / successfully, to get it washed

In this sentence, the idea is that the stain cannot be completely washed out without a good detergent. That completed result is expressed better with oprati.

You could use prati, but it would sound more like cannot wash it in general, without the clear idea of “get it fully out.” Oprati is the more natural choice here.

Who is the subject of ne mogu oprati if no pronoun (like ja) is written?

Croatian often drops the subject pronoun when it’s clear from context and verb form. Mogu can be:

ja mogu – I can
oni mogu – they can

Here, logically, the socks are not doing the washing. So the most natural reading is:

(Ja) ne mogu oprati – I cannot wash (it).

In context, it could also mean you or we (used generically), but grammatically, the subject pronoun is simply omitted because it’s understood. If you want to make it explicit, you can say:

… mrlju koju ja ne mogu oprati … – adding ja for emphasis.

Why is ne placed before mogu and not before oprati?

In Croatian, the negation ne is placed before the finite (conjugated) verb, not before the infinitive.

conjugated verb: mogu
infinitive: oprati

So:

mogu oprati – I can wash
ne mogu oprati – I cannot wash

Putting ne before oprati (mogu ne oprati) would be wrong or would mean something different and very unnatural. The structure ne + finite verb + infinitive is the standard pattern.

Why is it bez dobrog deterdženta and not bez dobar deterdžent?

There are two things happening:

The preposition bez (without) always takes the genitive case.
The adjective and noun must agree in case, gender, and number.

The base forms are:

adjective: dobar (good) – masculine singular nominative
noun: deterdžent (detergent) – masculine singular nominative

After bez, both must be genitive singular masculine:

dobar → dobrog
deterdžent → deterdženta

So we get bez dobrog deterdženta.
Bez dobar deterdžent would be ungrammatical because both words stay in nominative instead of changing to genitive.

Why does deterdžent change to deterdženta?

Deterdženta is the genitive singular form of deterdžent.

The preposition bez (without) must be followed by genitive:

nominative: deterdžent
genitive: deterdženta

This pattern is common for many masculine nouns ending in a consonant:

student → studenta (gen.)
telefon → telefona (gen.)
deterdžent → deterdženta (gen.)

So bez deterdženta is the correct form after bez.

Could the sentence use koja instead of koju?

No, in this sentence you need koju, not koja.

Koja is nominative feminine singular (subject form).
Koju is accusative feminine singular (object form).

In koju ne mogu oprati, the relative pronoun is the object of oprati:

(Ne mogu oprati) što? → koju

So the correct case is accusative → koju.
Using koja here would be a case error.

Can I change the word order, for example: Njegove čarape imaju mrlju koju bez dobrog deterdženta ne mogu oprati?

Yes, that word order is possible and natural in Croatian. Word order is quite flexible, and you can move the phrase bez dobrog deterdženta around:

All of these are acceptable:

… mrlju koju ne mogu oprati bez dobrog deterdženta.
… mrlju koju bez dobrog deterdženta ne mogu oprati.

The basic rules still apply:

The relative clause must stay attached to mrlju.
You cannot separate bez from dobrog deterdženta.
Ne must stay directly before the finite verb (mogu).

So you can rearrange for emphasis, but not break those grammatical relationships.