Πρέπει να έχω γράψει λάθος τον ταχυδρομικό κώδικα στο γράμμα, γι’ αυτό το έβαλα στο γραμματοκιβώτιο αργότερα.

Here πρέπει does not mean obligation in the sense of I have to.
In this sentence, πρέπει να έχω γράψει means I must have written in the sense of a deduction or assumption.

So:

• Πρέπει να έχω γράψει λάθος... = I must have written ... wrongly / I must have written ... wrong

This is a very common Greek pattern:

• πρέπει να + perfect-like form = must have + past participle in English

For example:

• Πρέπει να έχει φύγει. = He/She must have left.
• Πρέπει να το ξέχασα. can also mean I must have forgotten it, though the structure is slightly different.

Έχω γράψει is the perfect form, made with έχω + the non-finite form of the verb (γράψει).

It is used here because the speaker is making a conclusion about a completed earlier action:

• έχω γράψει = have written
• with πρέπει να → must have written

If you said Πρέπει να έγραψα, that can also occur in Greek and can mean something similar in casual speech, but πρέπει να έχω γράψει is clearer and more explicitly corresponds to English must have written.

So the perfect works well because the mistake happened before the later action of mailing the letter.

Λάθος literally means mistake or wrong, but very often in Greek it is used adverbially, meaning:

• wrongly
• incorrectly
• by mistake

So:

• έχω γράψει λάθος τον ταχυδρομικό κώδικα = I have written the postal code wrong / incorrectly

This is very natural Greek.

Compare:

• Το έκανα λάθος. = I did it wrong.
• Το είπα λάθος. = I said it wrong.

So λάθος does not need a separate adverb ending to work like wrongly here.

Because it is the direct object of γράψει.

The speaker wrote the postal code, so that noun is what receives the action.

• ο ταχυδρομικός κώδικας = the postal code (nominative)
• τον ταχυδρομικό κώδικα = the postal code (accusative)

Greek marks direct objects with case, so after a verb like γράφω you often see the accusative:

• γράφω το όνομα = I write the name
• γράφω τη διεύθυνση = I write the address
• γράφω τον ταχυδρομικό κώδικα = I write the postal code

This is just normal masculine noun inflection.

The dictionary form is:

• ο κώδικας

But in the accusative singular it becomes:

• τον κώδικα

This pattern is common with masculine nouns in -ας:

• ο μαθητής → τον μαθητή is a different pattern
• ο άντρας → τον άντρα
• ο φύλακας → τον φύλακα
• ο κώδικας → τον κώδικα

So κώδικα is not a different word; it is the same noun in a different case.

Greek often uses σε in places where English may choose either in, on, or at, depending on context.

So:

• στο γράμμα literally is in/on the letter
• in natural English, here we understand it as on the letter, because postal codes are written on the outside of an envelope or letter

Greek is less strict than English about this kind of preposition in many contexts.
The important thing is that στο γράμμα tells you the place where the postal code was written.

Depending on context, γράμμα can mean:

• letter as a piece of mail
• sometimes letter as a character of the alphabet, though not here

Γι’ αυτό means:

• for that
• because of that
• that’s why
• for this reason

In this sentence, the most natural translation is:

• that’s why

It connects the first clause to the second:

• I must have written the postal code wrong on the letter, that’s why I put it in the mailbox later.

The apostrophe appears because για is shortened before αυτό:

• για αυτό → γι’ αυτό

This contraction is very common in writing.

Literally, it means:

• I put it in the mailbox

But in context it naturally means:

• I posted it
• I put it into the mailbox

Greek often uses a very ordinary verb like βάζω (to put) for actions that English might express with a more specific verb.

So:

• έβαλα το γράμμα στο γραμματοκιβώτιο = I put the letter in the mailbox
• in natural English: I mailed / posted the letter

Το is the direct object pronoun, meaning it.

It refers back to το γράμμα?
Actually, the sentence says στο γράμμα earlier, and γράμμα is neuter:

• το γράμμα = the letter

So:

• το έβαλα = I put it
• it = the letter

Because γράμμα is neuter, the pronoun is also neuter:

• το

This is very normal in Greek: object pronouns usually match the gender and number of the noun they refer to.

In Greek, weak object pronouns typically come before a finite verb.

So Greek says:

• το έβαλα = literally it I-put

not:

• έβαλα το ✘

This is one of the most important word-order habits to get used to in Greek.

Examples:

• Το είδα. = I saw it.
• Την πήρα. = I took her / I got it (depending on context)
• Τους μίλησα. = I spoke to them

So το έβαλα is completely standard Greek word order.

Γραμματοκιβώτιο literally means letter box and is a standard word for a mailbox/postbox.

Depending on region and context, Greek speakers may also use other expressions, but γραμματοκιβώτιο is perfectly normal and clear.

In this sentence it means the box where you drop mail for posting.

It is a neuter noun:

• το γραμματοκιβώτιο

And after σε it becomes:

• στο γραμματοκιβώτιο = in/into the mailbox

Greek word order is flexible, and adverbs like αργότερα (later) are often placed toward the end of the clause.

So:

• γι’ αυτό το έβαλα στο γραμματοκιβώτιο αργότερα

is a natural way to say:

• that’s why I put it in the mailbox later

Putting αργότερα at the end gives it a natural informational focus.
You could move it in some contexts, but the given order sounds normal.

Yes, in many real-life situations Greek speakers might say:

• Πρέπει να έγραψα λάθος τον ταχυδρομικό κώδικα...

This can also mean I must have written the postal code wrong.

However:

• πρέπει να έχω γράψει is more explicitly perfect-like
• it matches the English idea of must have written very neatly

So both can be possible, but the version with έχω γράψει highlights the completed past action more clearly.

Yes, the grammar is understandable and natural enough for a learner to study. It shows several common Greek features:

• πρέπει να for deduction
• the perfect έχω γράψει
• λάθος used adverbially
• object pronoun before the verb: το έβαλα
• γι’ αυτό to express cause/result

The logic is:

1. I must have written the postal code wrong on the letter
2. for that reason / that’s why I mailed it later

So the speaker is explaining a delay by referring to a likely earlier mistake.