Δεν ξέρω αν αυτή είναι η σωστή απάντηση.

Because Greek often drops subject pronouns when the verb ending already shows who the subject is.

• ξέρω = I know
• The ending -ω tells you it is 1st person singular.

So Δεν ξέρω already means I don’t know.
You could say Εγώ δεν ξέρω, but that adds emphasis, like I don’t know.

Δεν is the normal negation used with verbs in the indicative mood.

So:

• ξέρω = I know
• δεν ξέρω = I do not know

A learner may confuse δεν with μη(ν), but μη(ν) is used in different environments, such as commands, wishes, or after certain particles like να.

In this sentence, δεν is the correct choice because this is a straightforward statement.

Here αν means if / whether.

In English, we often distinguish:

• if this is the right answer
• whether this is the right answer

In Greek, αν commonly covers both ideas in sentences like this.

So:

• Δεν ξέρω αν... = I don’t know if / whether...

Because αυτή is the subject of είναι, so it is in the nominative case.

• αυτή = this / she (nominative feminine singular)
• αυτήν = this / her (accusative feminine singular)

In this sentence:

• αυτή είναι... = this is...

So Greek uses the nominative form αυτή.

It is feminine because it refers to η απάντηση, and απάντηση is a feminine noun in Greek.

Greek words that refer to the same thing usually have to agree in gender, number, and case where appropriate.

So:

• αυτή = feminine singular
• η σωστή απάντηση = feminine singular

They match because they refer to the same thing.

Because Greek uses the definite article much like English uses the.

• η απάντηση = the answer
• η σωστή απάντηση = the right/correct answer

The article must agree with the noun:

• η = feminine singular nominative
• απάντηση = feminine singular nominative

So η is there for the same basic reason English uses the in the right answer.

Because adjectives in Greek must agree with the noun they describe.

The noun here is:

• η απάντηση = feminine singular

So the adjective must also be feminine singular nominative:

• masculine: σωστός
• feminine: σωστή
• neuter: σωστό

Therefore:

• η σωστή απάντηση = the correct answer

Because they are linked by the verb είναι (to be).

With to be, Greek normally puts both the subject and the predicate noun phrase in the nominative:

• αυτή = nominative
• η σωστή απάντηση = nominative

This is similar to the logic of English This is the right answer, where both parts are being equated.

Είναι is the 3rd person singular (and also 3rd person plural) present tense form of είμαι = to be.

Here it means is:

• αυτή είναι... = this is...

So the structure is:

• Δεν ξέρω = I don’t know
• αν αυτή είναι... = if this is...

Yes, Greek word order is often more flexible than English, though not completely free.

This sentence is the most neutral, natural order:

• Δεν ξέρω αν αυτή είναι η σωστή απάντηση.

But other orders are possible depending on emphasis, for example:

• Δεν ξέρω αν η σωστή απάντηση είναι αυτή.
  = I don’t know if this is the right answer / if the right answer is this one.

That version shifts the focus a bit.

So the original order is standard and natural, but Greek can move things around for emphasis.

In this sentence, it is best understood as this.

Formally, αυτή can also mean she, depending on context. But here, because the sentence talks about the right answer, the natural interpretation is demonstrative:

• αυτή = this (one)

So the idea is I don’t know if this is the right answer, not I don’t know if she is the right answer.

It does — that word here is σωστή.

A common point for English speakers is that English right has many meanings:

• correct
• right-side opposite of left
• morally right

Greek usually uses different words depending on the meaning.
Here σωστή means correct, not right-hand.

So:

• η σωστή απάντηση = the correct answer

You can, but it changes the meaning slightly.

• η σωστή απάντηση = the correct answer
• σωστή απάντηση = a correct answer / correct answer depending on context

In your sentence, the article makes it sound like there is a specific answer being evaluated as the correct one. That matches the English sentence naturally.

Yes. Ξέρω is the normal everyday verb for know in the sense used here.

Greek also has γνωρίζω, but that is often used for:

• knowing a person
• being acquainted with
• formally knowing / recognizing

In a sentence like I don’t know if this is the right answer, ξέρω is exactly the natural choice.

If you want to emphasize this, Greek can do that with stress or word order.

For example:

• Δεν ξέρω αν αυτή είναι η σωστή απάντηση.
  Neutral, natural.
• Δεν ξέρω αν αυτή είναι η σωστή απάντηση, όχι κάποια άλλη.
  Stronger contrast: this one, not another one.

Often the main emphasis in speech comes from intonation, not just word order. So even the original sentence can strongly stress αυτή when spoken.