Έβαλα τη χειραποσκευή κάτω από το κάθισμα πριν από την απογείωση.

Έβαλα is the aorist form of βάζω (to put).
In this sentence, it means I put in the sense of I placed it as a completed action.

So:

• βάζω = I put / I am putting
• έβαλα = I put / I placed

Greek often uses the aorist when talking about a single completed action in the past.

Βάζω / έβαλα is the most common everyday verb for put / place in spoken Greek. It is very natural here.

Θέτω / έθεσα exists, but it is much more formal and is often used in abstract meanings, such as:

• θέτω μια ερώτηση = pose a question
• θέτω όρους = set conditions

For physically putting a bag somewhere, βάζω is the normal choice.

τη χειραποσκευή is in the accusative case because it is the direct object of Έβαλα.

You put what?
→ τη χειραποσκευή

So:

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

In Modern Greek, the direct object usually takes the accusative.

Both τη and την are common spellings/pronunciations of the feminine accusative article.

Before a consonant, Greek very often drops the final -ν in everyday usage:

• τη χειραποσκευή
• την απογείωση

Why does την απογείωση keep the -ν? Because the next word begins with a vowel (α).

A helpful rule of thumb:

• before vowels: usually την
• before many consonants: often τη

So τη χειραποσκευή is completely normal.

Η χειραποσκευή means carry-on bag, hand luggage, or cabin baggage.

It is a feminine noun:

• nominative: η χειραποσκευή
• accusative: τη χειραποσκευή
• plural: οι χειραποσκευές

It is a compound word related to the idea of baggage carried by hand.

In this expression, κάτω από means under / below.

Literally:

• κάτω = down / below
• από = from

But together, κάτω από functions as a fixed expression meaning under:

• κάτω από το τραπέζι = under the table
• κάτω από το κάθισμα = under the seat

So you should learn κάτω από as one location phrase, not word by word.

After κάτω από, the noun is normally in the accusative.

So:

• nominative: το κάθισμα
• accusative: το κάθισμα

This noun is neuter, and in this case the form happens to look the same in nominative and accusative. The article το also stays the same.

That is why you see:

• κάτω από το κάθισμα = under the seat

Yes, very often you can say just πριν.

Both are used:

• πριν από την απογείωση
• πριν την απογείωση
• sometimes simply πριν

In this sentence, πριν από την απογείωση is a very standard and clear way to say before takeoff.

So πριν από is a common prepositional expression meaning before.

Because πριν από is followed by the accusative.

So:

• nominative: η απογείωση = takeoff
• accusative: την απογείωση

This is very common with Greek prepositions and prepositional expressions: they often require a specific case, and here that case is accusative.

Yes. Απογείωση means takeoff, and it is related to the verb απογειώνομαι (to take off).

Examples:

• Η απογείωση καθυστέρησε. = The takeoff was delayed.
• Το αεροπλάνο απογειώθηκε. = The plane took off.

So in your sentence, πριν από την απογείωση means before takeoff.

The sentence is natural as it stands, but Greek word order is more flexible than English.

This version:

• Έβαλα τη χειραποσκευή κάτω από το κάθισμα πριν από την απογείωση.

is neutral and natural.

You might also hear variations for emphasis, such as:

• Πριν από την απογείωση, έβαλα τη χειραποσκευή κάτω από το κάθισμα.
• Τη χειραποσκευή την έβαλα κάτω από το κάθισμα πριν από την απογείωση.

The basic meaning stays the same, but the focus can shift slightly.

A rough pronunciation guide is:

EVALA ti hiri-aposkeVÍ KÁto apó to KÁthisma prin apó tin apojÍosi

A few notes:

• Έβαλα stress on the first syllable: É-va-la
• χειραποσκευή stress on the last syllable: hi-ra-po-ske-VÍ
• κάτω stress on the first syllable: KÁ-to
• κάθισμα stress on the first syllable: KÁ-this-ma
• απογείωση stress on -γεί-: a-po-GÍ-o-si

Also:

• χ is like the h in Bach or the German ch, not like English ch
• θ is like English th in think

Because από appears inside two different fixed expressions:

• κάτω από = under
• πριν από = before

Even though it is the same word, it is doing different jobs as part of two common multi-word expressions. This is completely normal in Greek.

Not in this context if you mean an airplane seat.

• κάθισμα = seat
• καρέκλα = chair

On a plane, κάθισμα is the correct word.
So κάτω από το κάθισμα is exactly what you would expect for under the seat.

Yes, it sounds very natural.

It fits a typical airline or travel situation, especially because passengers are often told to place hand luggage κάτω από το κάθισμα before takeoff.

So the vocabulary and structure are both realistic and idiomatic.