Ξέχασα την πετσέτα μου στα αποδυτήρια του γυμναστηρίου.

Greek often drops subject pronouns when they are not needed, because the verb ending already shows the person.

Here, Ξέχασα means I forgot. The ending -α tells you it is 1st person singular.

So:

• Ξέχασα = I forgot
• Εγώ ξέχασα = I forgot too, but with extra emphasis on I

You would add εγώ only if you wanted contrast or emphasis, like I forgot it, not you.

Ξέχασα is the aorist form of ξεχνάω / ξεχνώ.

In this sentence, it means a completed past action:

• ξεχνάω = I forget / I am forgetting
• ξέχασα = I forgot

So the sentence is talking about one specific past event: forgetting the towel.

In Greek, it is very normal to use the definite article with possessed nouns.

So Greek says:

• την πετσέτα μου = literally the towel my
• natural English = my towel

This is standard Greek structure. English usually does not use the before my, but Greek usually does.

Because πετσέτα is:

• feminine
• singular
• the direct object of the verb

So it must be in the accusative singular feminine form.

That gives:

• nominative: η πετσέτα = the towel (subject form)
• accusative: την πετσέτα = the towel (object form)

Since it is the thing that was forgotten, Greek uses the accusative: την πετσέτα.

In Greek, short possessive words like μου, σου, του, της often come after the noun.

So:

• η πετσέτα μου = my towel
• το βιβλίο σου = your book

Here, μου means my, because it follows a noun and shows possession.

The same word μου can also mean to me or of me in other contexts, but after a noun like πετσέτα, it is normally understood as possessive.

στα is a contraction of:

• σε = in / at / to
• τα = the (neuter plural accusative)

So:

• σε τα → στα

Here, στα αποδυτήρια means in the changing rooms / in the locker room area.

This kind of contraction is very common in Greek:

• σε + το = στο
• σε + τη(ν) = στη(ν)
• σε + τα = στα

Because αποδυτήρια is commonly used in Greek as a plural noun for changing rooms / locker rooms.

So even if English might say the locker room, Greek often says τα αποδυτήρια.

This is just one of those cases where Greek and English organize the idea differently:

• Greek: στα αποδυτήρια
• English: in the locker room or in the changing rooms

Both are natural in their own language.

του γυμναστηρίου is in the genitive case and means of the gym.

It tells you which changing rooms:

• τα αποδυτήρια = the changing rooms
• τα αποδυτήρια του γυμναστηρίου = the gym’s changing rooms / the changing rooms of the gym

So του γυμναστηρίου modifies αποδυτήρια.

Also note:

• το γυμναστήριο = nominative
• του γυμναστηρίου = genitive

Yes. Greek word order is more flexible than English, because the case endings and articles help show what each word is doing.

The given sentence is a natural, neutral version:

• Ξέχασα την πετσέτα μου στα αποδυτήρια του γυμναστηρίου.

But you could also say:

• Την πετσέτα μου ξέχασα στα αποδυτήρια του γυμναστηρίου.
  This puts more focus on the towel.
• Στα αποδυτήρια του γυμναστηρίου ξέχασα την πετσέτα μου.
  This puts more focus on where it happened.

So the meaning stays basically the same, but the emphasis can change.

In this context, it strongly suggests I left it behind because I forgot it.

So in natural English, it can correspond to:

• I forgot my towel in the locker room
• I left my towel in the locker room

Greek ξεχνάω / ξέχασα can work this way when the context makes it clear that an object was forgotten somewhere.

Grammatically, yes, if you really mean the changing room in the singular:

• στο αποδυτήριο του γυμναστηρίου

But in everyday Greek, τα αποδυτήρια is often the more idiomatic choice for this kind of place.

So:

• στα αποδυτήρια του γυμναστηρίου = very natural
• στο αποδυτήριο του γυμναστηρίου = possible, but less common in many contexts

A useful breakdown is:

• Ξέχασα = I forgot
• την πετσέτα μου = my towel
• στα αποδυτήρια = in the changing rooms / locker room
• του γυμναστηρίου = of the gym

So the structure is:

verb + direct object + place phrase + genitive phrase

More literally:

• I-forgot the towel my in-the changing-rooms of-the gym

That may look strange from an English point of view, but it is completely normal Greek structure.