Δεν ξέρω αν δικαιούμαι άλλη άδεια, αλλά θα ρωτήσω τη λογίστρια το απόγευμα.

Both ξέρω and γνωρίζω can relate to knowing, but they are used differently.

• ξέρω = I know, I know how, I am aware
• γνωρίζω = I know / am acquainted with, often for people, places, or facts in a slightly more formal style

In this sentence, Δεν ξέρω αν... is the natural everyday way to say I don’t know if / whether...

So:

• Δεν ξέρω αν δικαιούμαι... = I don’t know if I’m entitled...

Using γνωρίζω here would sound more formal and less conversational.

Here αν means if / whether in the sense of introducing an indirect question.

So:

• Δεν ξέρω αν δικαιούμαι άλλη άδεια
  = I don’t know if / whether I’m entitled to more leave

This is very common in Greek:

• Δεν ξέρω αν έρχεται. = I don’t know if he’s coming.
• Ρώτα αν είναι ανοιχτά. = Ask whether they’re open.

Greek uses αν in places where English often uses whether.

δικαιούμαι comes from the verb δικαιούμαι, which means to be entitled to, to have the right to receive, or sometimes to deserve depending on context.

This is one of those Greek verbs that looks like a passive/middle form because it ends in -ούμαι, but its meaning is active in English:

• δικαιούμαι άδεια = I’m entitled to leave
• δικαιούσαι έκπτωση = you are entitled to a discount

So δικαιούμαι is:

• 1st person singular
• present tense
• meaning I am entitled

Even though the form looks passive, you should learn it as the normal dictionary form of the verb.

Greek usually does not need subject pronouns because the verb ending already shows the person.

• ξέρω = I know
• δικαιούμαι = I am entitled
• ρωτήσω = I ask / I will ask in this future structure

So Greek often leaves out εγώ (I) unless it is needed for emphasis or contrast.

For example:

• Δεν ξέρω... = I don’t know...
• Εγώ δεν ξέρω, αλλά εκείνος ξέρει. = I don’t know, but he does.

In your sentence, no pronoun is needed.

άλλη means another or more / additional, depending on context.

Here:

• άδεια = leave, time off, permit
• άλλη άδεια = more leave / another leave period / additional leave

Grammatically, άλλη agrees with άδεια:

• άδεια is feminine singular
• so the adjective is also feminine singular: άλλη

Compare:

• άλλος άνθρωπος = another person (masculine)
• άλλη μέρα = another day (feminine)
• άλλο θέμα = another issue (neuter)

In this sentence, άλλη άδεια most naturally means additional leave.

άδεια is a very common Greek word with several related meanings:

• leave / time off from work
• permission
• license / permit

In this sentence, because of the work-related context and the mention of the accountant, it most likely means leave from work.

Examples:

• πήρα άδεια = I took leave / I took time off
• άδεια μητρότητας = maternity leave
• άδεια οδήγησης = driving license
• με την άδειά σας = with your permission

So context is very important with this word.

Greek often uses two different stems for a verb:

• an imperfective form for ongoing/repeated action
• a perfective form for a single complete action

Here:

• ρωτάω / ρωτώ = I ask, I am asking (imperfective)
• ρωτήσω = perfective subjunctive form used after θα

So:

• θα ρωτήσω = I will ask
  one complete action: I’ll ask her later

If you said θα ρωτάω, it would suggest something more like:

• I will be asking
• I will ask repeatedly / habitually

So θα ρωτήσω is the natural choice for I’ll ask in this sentence.

Because λογίστρια is the direct object of the verb ρωτήσω.

• η λογίστρια = the accountant as subject
• τη(ν) λογίστρια = the accountant as object

In the sentence:

• θα ρωτήσω τη λογίστρια = I’ll ask the accountant

Greek marks this difference with case:

• nominative: η λογίστρια
• accusative: τη(ν) λογίστρια

So the article changes because the noun is receiving the action.

Both spellings may appear, depending on style and pronunciation habits, but in everyday modern Greek, the final -ν of την is often dropped before certain consonants.

So:

• την λογίστρια
• τη λογίστρια

Both can be seen, but τη λογίστρια is very normal.

A simple rule learners often use:

The final -ν is more likely to stay before vowels and certain consonants, and often drops before others in everyday writing and speech.

So don’t be surprised by both forms.

Yes. Greek works the same way here.

• ρωτάω κάποιον = ask someone
• ρωτάω κάτι = ask something
• ρωτάω κάποιον κάτι = ask someone something

So:

• θα ρωτήσω τη λογίστρια = I’ll ask the accountant
• θα ρωτήσω τη λογίστρια αν δικαιούμαι άλλη άδεια = I’ll ask the accountant if I’m entitled to more leave

This is very straightforward and common Greek usage.

Yes, απόγευμα is a noun meaning afternoon, but Greek often uses the article with time expressions.

So:

• το απόγευμα = in the afternoon / this afternoon

In your sentence:

• θα ρωτήσω τη λογίστρια το απόγευμα
  = I’ll ask the accountant this afternoon

This is a very common pattern:

• το πρωί = in the morning / this morning
• το βράδυ = in the evening / tonight
• τη Δευτέρα = on Monday

So even though English often drops the article, Greek frequently keeps it.

Greek word order is more flexible than English, because case endings and verb forms already show a lot of grammatical information.

The given sentence is neutral and natural:

• Δεν ξέρω αν δικαιούμαι άλλη άδεια, αλλά θα ρωτήσω τη λογίστρια το απόγευμα.

But other orders are also possible for emphasis:

• Δεν ξέρω αν δικαιούμαι άλλη άδεια, αλλά το απόγευμα θα ρωτήσω τη λογίστρια.
• Αλλά θα ρωτήσω τη λογίστρια το απόγευμα.
• Τη λογίστρια θα ρωτήσω το απόγευμα.
  This puts extra emphasis on the accountant

So yes, the order can change, but the original version is the most neutral everyday phrasing.

αλλά means but.

It connects two ideas:

1. Δεν ξέρω αν δικαιούμαι άλλη άδεια = I don’t know if I’m entitled to more leave
2. θα ρωτήσω τη λογίστρια το απόγευμα = I’ll ask the accountant this afternoon

So the meaning is:

• I don’t know..., but I’ll ask...

This is the normal Greek conjunction for contrast.

δικαιούμαι is pronounced roughly like:

• dhee-keh-YOO-meh

The stressed syllable is ού.

The sequence αι is usually pronounced like e, and ού is pronounced oo.

So the word breaks approximately like this:

• δι-και-ού-μαι

Even though there are several vowels written together, Greek spelling often preserves the historical form of the word, while pronunciation is more streamlined than it may first appear.

It is neutral, natural modern Greek.

It is not especially informal, and not especially formal either. It sounds like something someone could say in everyday life, especially in a workplace context.

A few things that make it sound natural and standard:

• Δεν ξέρω αν...
• θα ρωτήσω...
• το απόγευμα

So this is a good model sentence for normal spoken and written Greek.