Εκείνη παρεξήγησε το αστείο, αλλά μετά γελάσαμε μαζί.

Yes. Εκείνη is the feminine form of εκείνος / εκείνη / εκείνο, which can mean:

• that one
• she (with emphasis)

In this sentence, Εκείνη means she, but it is a bit more explicit or emphatic than simply leaving the subject unstated.

Greek often drops subject pronouns because the verb ending already shows the person. So instead of:

• Εκείνη παρεξήγησε...

Greek could also say:

• Παρεξήγησε...

Using Εκείνη helps highlight the contrast with the later we in γελάσαμε.

Παρεξήγησε means misunderstood.

It is the aorist (simple past), 3rd person singular, from the verb παρεξηγώ = to misunderstand.

So:

• παρεξηγώ = I misunderstand / I am misunderstanding
• παρεξήγησε = she/he misunderstood

This tense is used for a completed event in the past: she misunderstood the joke.

Many Greek verbs change stem in the aorist, and παρεξηγώ is one of them.

You can think of it like this:

• present stem: παρεξηγ- / παρεξηγώ
• aorist stem: παρεξήγησ-

Then the ending -ε gives he/she/it:

• παρεξήγησε = he/she/it misunderstood

This kind of stem change is common in Greek and usually just has to be learned with the verb.

Here, το αστείο is a noun phrase meaning the joke.

That is because αστείο can be:

• an adjective: funny
• a noun: joke

In this sentence, the article το shows that it is being used as a noun:

• το αστείο = the joke

Compare:

• Ήταν αστείο. = It was funny.
• Δεν κατάλαβα το αστείο. = I didn’t get the joke.

Greek uses articles very frequently, often more regularly than English.

Here, το αστείο means the joke. The article is natural because the speaker is referring to a specific joke already understood in the context.

Greek articles also show gender, number, and case:

• το = neuter singular nominative/accusative
• αστείο is neuter singular

Since παρεξήγησε takes a direct object, το αστείο is in the accusative, but for neuter singular the nominative and accusative look the same.

αλλά means but.
μετά means afterwards / then / later.

So:

• αλλά μετά = but then / but afterwards

This combination shows a change in the situation:

1. first she misunderstood the joke
2. but then later, something changed
3. we laughed together

It is very natural Greek.

Γελάσαμε means we laughed.

It is the aorist, 1st person plural, from γελάω or γελώ = to laugh.

So:

• γελάω / γελώ = I laugh
• γελάσαμε = we laughed

The ending -σαμε is a very common aorist ending for we.

Because the meaning is:

• She misunderstood the joke
• but then we laughed together

The first clause has she as the subject: Εκείνη παρεξήγησε...
The second clause has we as the subject, shown by the verb ending: γελάσαμε.

Greek does not need to say εμείς (we) because γελάσαμε already clearly means we laughed.

The switch in subject is completely normal.

Μαζί means together.

So:

• γελάσαμε μαζί = we laughed together

It is not strictly necessary if context already makes that obvious, but it adds the idea that the laughter was shared.

Without μαζί:

• μετά γελάσαμε = then we laughed

With μαζί:

• μετά γελάσαμε μαζί = then we laughed together

Yes. Greek word order is more flexible than English.

The sentence as given is very natural:

• Εκείνη παρεξήγησε το αστείο, αλλά μετά γελάσαμε μαζί.

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

• Παρεξήγησε το αστείο εκείνη, αλλά μετά γελάσαμε μαζί.
• Μετά γελάσαμε μαζί, αλλά εκείνη παρεξήγησε το αστείο.
  (This changes the flow and emphasis.)

The original order is probably the most neutral and clear for a learner.

Because Greek usually leaves subject pronouns out unless they are needed for emphasis or contrast.

So:

• γελάσαμε already means we laughed

If you said:

• αλλά μετά εμείς γελάσαμε μαζί

that would sound more emphatic, as if contrasting we with someone else.

In most ordinary sentences, Greek prefers just the verb.

A rough pronunciation guide is:

• Εκείνη → eh-KEE-nee
• παρεξήγησε → pa-rek-SEE-yee-se
• το αστείο → to a-STEE-o
• αλλά μετά → a-LA me-TA
• γελάσαμε μαζί → ye-LA-sa-me ma-ZEE

A few useful notes:

• γ before ε / ι sounds like a soft sound, somewhat like y in this sentence
• the stressed syllable is marked by the written accent:
  • Εκείνη
  • παρεξήγησε
  • αστείο
  • μετά
  • γελάσαμε
  • μαζί

Yes: it tells a small story with a contrast and a positive resolution.

• Εκείνη παρεξήγησε το αστείο = something awkward happened
• αλλά μετά γελάσαμε μαζί = the awkwardness was resolved

So the sentence sounds natural and conversational, and αλλά μετά helps create that narrative turn: first misunderstanding, then shared laughter.