Μετά τη φωτογράφιση, η νύφη άφησε το πέπλο στο αυτοκίνητο και γύρισε για να το πάρει.

Because μετά takes the accusative in Modern Greek when it means after.

• η φωτογράφιση = the photo shoot / photo session (nominative, the dictionary form with the article)
• τη φωτογράφιση = the photo shoot / photo session (accusative)

So:

• Μετά τη φωτογράφιση = After the photo shoot

Also, you may notice τη instead of την. The feminine accusative article is often written as τη(ν). The final -ν is dropped before many consonants, and φ in φωτογράφιση is one of those cases, so τη φωτογράφιση is normal.

In Greek, the definite article is used very often with nouns, much more than in English. With a specific person or thing, it is normally required.

So:

• η νύφη = the bride

Leaving out the article here would sound unnatural in standard Greek.

Άφησε is the aorist form of αφήνω (to leave).

Here it expresses a completed past action:

• άφησε το πέπλο = she left the veil

Greek often uses the aorist in storytelling to describe one completed action after another.

Στο is a contraction of:

• σε = in / to / at
• το = the

So:

• σε το αυτοκίνητο becomes στο αυτοκίνητο

Here it means in the car (or sometimes to the car, depending on context, but here in the car is the natural meaning).

Because το later in the sentence is a direct object pronoun meaning it.

• το πέπλο = the veil
• να το πάρει = to get it

The pronoun matches πέπλο, which is neuter singular, so the pronoun is also το.

In Modern Greek, weak object pronouns like το, τη, τον, τα normally come before the verb.

So Greek says:

• να το πάρει = literally to it take

But in natural English, of course, this becomes to get it.

This is one of the most common word-order differences between Greek and English.

Here γύρισε means went back / returned, not just physically turned around.

The verb γυρίζω can mean different things depending on context:

• turn
• go back
• return

In this sentence, because she had left something in the car and then went back to get it, γύρισε is best understood as returned or went back.

Για να introduces purpose and means:

• in order to
• so that
• often simply to

So:

• γύρισε για να το πάρει = she went back in order to get it

It shows why she returned.

Because after να (and για να), Greek uses the subjunctive, not an ordinary past tense form.

So:

• πήρε = she took / she got (past, independent statement)
• να πάρει = to get / so that she gets (subjunctive form after να)

Even though the whole sentence is in the past, πάρει stays in the subjunctive because it depends on για να.

Greek often leaves out a possessive like her when possession is already clear from the context.

So:

• το πέπλο = the veil
• in this context, we naturally understand it is her veil

Greek frequently uses the article where English might prefer a possessive.

Yes. Greek is a pro-drop language, which means the subject pronoun or even the subject noun can often be omitted if the verb form and context make it clear.

So this would also be possible:

• Μετά τη φωτογράφιση, άφησε το πέπλο στο αυτοκίνητο και γύρισε για να το πάρει.

That still means After the photo shoot, she left the veil in the car and went back to get it.

The full η νύφη is included for clarity, emphasis, or simply because the speaker wants to mention the bride explicitly.

Yes, that is also possible in many contexts.

• γύρισε να το πάρει
• γύρισε για να το πάρει

Both can mean she went back to get it.

Very roughly:

• να alone can sound a bit more direct or conversational
• για να can sound a bit more explicit about purpose

In this sentence, για να is perfectly natural and clearly shows intention.

Because the sentence narrates two completed actions in sequence:

1. she left the veil in the car
2. she went back to get it

Greek commonly uses the aorist for this kind of storyline. It is the normal tense for reporting single completed events in the past.

So the structure is very natural:

• άφησε = she left
• γύρισε = she went back / returned

Both are completed past actions.