Learn Hardcore Greek: Σήμερα όμως δεν μπορώ να δεχτώ άλλη πρόσκληση, είμαι κουρασμένος. - Today however I can’t accept another invitation, I am tired male.

If you put όμως first (Όμως σήμερα…), the contrast can feel a bit more general, like starting a new thought with However, and then specifying today.

Why is the negation δεν placed before μπορώ and not before δεχτώ?

In Greek, δεν normally comes right before the finite verb (the conjugated verb that carries tense/person):

δεν μπορώ = I cannot

The structure here is:

δεν μπορώ (finite verb, present: I cannot)
να δεχτώ (subjunctive form: to accept)

So we negate μπορώ, not δεχτώ.
You would not say μπορώ δεν να δεχτώ or μπορώ να δεν δεχτώ—those are ungrammatical.

Why do we say να δεχτώ after μπορώ? Why not just a plain “infinitive” like in English (“I cannot accept”)?

Modern Greek does not have an infinitive like English to accept.
Instead, Greek uses να + subjunctive:

να δεχτώ ≈ to accept (in this context)

After many verbs like μπορώ (can), θέλω (want), πρέπει (must), you use να + subjunctive:

μπορώ να δεχτώ = I can accept
θέλω να φύγω = I want to leave
πρέπει να διαβάσω = I must study

So δεν μπορώ να δεχτώ is the natural Greek equivalent of I cannot accept.

What is the difference between δεχτώ and δεχθώ? Which one is more correct?

Both δεχτώ and δεχθώ are correct forms of the aorist subjunctive of δέχομαι (to accept).

δεχτώ is more common in everyday speech.
δεχθώ sounds a bit more formal or careful and is closer to the older, more “learned” form.

Meaning-wise, in a sentence like δεν μπορώ να δεχτώ άλλη πρόσκληση, there is no real difference. Most native speakers would naturally say δεχτώ here.

Why is it άλλη πρόσκληση and not something like άλλος πρόσκληση?

Πρόσκληση is a feminine noun in the singular nominative/accusative:

η πρόσκληση = the invitation

The adjective άλλος (other / another) must agree in gender, number, and case with the noun:

Masculine: άλλος φίλος (other male friend)
Feminine: άλλη φίλη / άλλη πρόσκληση (other female friend / other invitation)
Neuter: άλλο βιβλίο (other book)

Here we have a feminine noun in the accusative singular (πρόσκληση as the direct object), so we use the matching feminine form άλλη:

άλλη πρόσκληση = another invitation

Why is there no article before άλλη πρόσκληση? Why not μια άλλη πρόσκληση?

Both are possible, but without the article is more natural here.

άλλη πρόσκληση = another invitation (general)
μια άλλη πρόσκληση = one more / one other invitation (often slightly more specific or counting-like)

In everyday speech, when you mean another/any more invitation in a general way, Greeks often just use άλλη without μια:

Δεν μπορώ να δεχτώ άλλη πρόσκληση
= I can’t accept another invitation / any more invitations.

Adding μια would not be wrong; it just feels a bit more like one more rather than any more.

What is the function of the comma before είμαι κουρασμένος? Could this be two separate sentences?

Yes, it could be written as two separate sentences:

Σήμερα όμως δεν μπορώ να δεχτώ άλλη πρόσκληση. Είμαι κουρασμένος.

The comma here simply connects two closely related clauses:

first: the refusal (I can’t accept another invitation)
second: the reason or accompanying state (I am tired)

Greek often uses commas where English might use either a new sentence, because, or since. So this comma is like saying:

Today, however, I can’t accept another invitation, (because) I’m tired.

If the speaker is a woman, does είμαι κουρασμένος change?

Yes. Κουρασμένος is a masculine adjective form.

Masculine speaker: είμαι κουρασμένος (I am tired)
Feminine speaker: είμαι κουρασμένη

So a woman would say:

Σήμερα όμως δεν μπορώ να δεχτώ άλλη πρόσκληση, είμαι κουρασμένη.

What is the difference between κουρασμένος and a verb like κουράζομαι?

κουράζομαι = I get tired / I tire (myself) (verb, present)
κουράστηκα = I got tired (aorist)
κουρασμένος = tired (past participle used as an adjective)

In the sentence, είμαι κουρασμένος uses the adjective form κουρασμένος with the verb είμαι (to be), literally I am tired.

So:

Κουράστηκα, είμαι κουρασμένος.
= I got tired, I am tired.

Why is σήμερα at the beginning? Can I move it, like Δεν μπορώ σήμερα να δεχτώ άλλη πρόσκληση?

You can move σήμερα; Greek word order is flexible, with differences in emphasis:

Σήμερα όμως δεν μπορώ να δεχτώ άλλη πρόσκληση…
Focuses on today as the setting: Today, however, I can’t…
Δεν μπορώ σήμερα να δεχτώ άλλη πρόσκληση…
Puts a bit more emphasis on the inability today.
Δεν μπορώ να δεχτώ άλλη πρόσκληση σήμερα…
Feels very close to English I can’t accept another invitation today.

All are grammatically correct; the original just foregrounds σήμερα for emphasis.

Could we say δεν μπορώ να αποδεχτώ άλλη πρόσκληση instead of να δεχτώ? Is there a difference?

Yes, you can say:

δεν μπορώ να αποδεχτώ άλλη πρόσκληση

Αποδέχομαι / αποδεχτώ also means to accept, but:

δέχομαι / δεχτώ is more general and more common in everyday speech.
αποδέχομαι / αποδεχτώ can sound more formal or official, often used with things like terms, conditions, proposals, apologies, etc.

For invitations, δεχτώ is the most natural, conversational choice.