Σήμερα δεν έχω ούτε καν δέκα λεπτά ελεύθερα, γι’ αυτό θα σου απαντήσω αργότερα.

Σήμερα means today, and it works as an adverb of time. Greek often puts time words near the beginning of the sentence to set the scene first.

So:

• Σήμερα δεν έχω... = Today I don’t have...

This is very natural in Greek, just like in English. You could move it, but the original order sounds completely normal and emphasizes today as the relevant time frame.

Greek normally negates the verb directly with δεν.

• έχω = I have
• δεν έχω = I do not have / I don’t have

So the negative starts at the verb. After that, Greek can add other negative-style expressions such as ούτε καν for stronger emphasis.

ούτε καν means not even.

In this sentence:

• δεν έχω ούτε καν δέκα λεπτά ελεύθερα
  = I don’t even have ten free minutes

It strengthens the idea: the speaker is so busy that they do not have even that small amount of time.

A useful breakdown:

• ούτε = not even / neither
• καν = adds emphasis, something like even at all

Together, ούτε καν is a very common phrase meaning not even.

Yes, but that is normal in Greek.

English usually avoids this kind of structure in standard usage, but Greek commonly uses negative concord, where more than one negative element appears in the same sentence.

So:

• δεν έχω ούτε καν δέκα λεπτά
  literally looks like I don’t have not-even ten minutes
• but it simply means
  I don’t even have ten minutes

This is standard Greek grammar, not a mistake.

Because the phrase is indefinite: ten minutes, not the ten minutes.

Greek often leaves out the article with numbers when you are simply stating an amount:

• δέκα λεπτά = ten minutes
• δύο ώρες = two hours
• πέντε μέρες = five days

So δέκα λεπτά is exactly what you would expect here.

λεπτά is the plural of λεπτό (minute).

• singular: το λεπτό = the minute
• plural: τα λεπτά = the minutes

After a number greater than one, Greek uses the plural:

• ένα λεπτό = one minute
• δέκα λεπτά = ten minutes

Here δέκα λεπτά is in the accusative plural, which is also the form you use after έχω in this kind of sentence.

Because ελεύθερα agrees with λεπτά, and λεπτά is neuter plural.

• λεπτό is neuter
• plural: λεπτά
• adjective must match in gender, number, and case

So:

• δέκα λεπτά ελεύθερα = ten free minutes

Compare:

• ένας ελεύθερος άνθρωπος = a free man
• μια ελεύθερη θέση = a free seat
• δέκα ελεύθερα λεπτά or δέκα λεπτά ελεύθερα = ten free minutes

Yes, it can often go before or after, but the position can sound a little different stylistically.

Here:

• δέκα λεπτά ελεύθερα

is very natural and idiomatic, especially when meaning ten minutes available/free.

You may also hear:

• δέκα ελεύθερα λεπτά

Both are possible, but with time expressions Greek very often places the adjective after the noun in this kind of phrase.

No. Here it means free/available, as in unoccupied or not busy.

So:

• ελεύθερα λεπτά = free minutes / available minutes

It does not mean the minutes cost nothing. The context makes that clear: the speaker is talking about time they have available.

γι’ αυτό means for that / because of that / therefore / that’s why. In this sentence, the best English equivalent is that’s why or so.

The full form is για αυτό, but it is very commonly contracted in writing to γι’ αυτό.

So:

• ..., γι’ αυτό θα σου απαντήσω αργότερα.
• ..., that’s why I’ll answer you later.

It links the second clause to the first: because the speaker has no time now, they will reply later.

The apostrophe shows contraction.

• full form: για αυτό
• contracted form: γι’ αυτό

This is very common in Greek when για is shortened before a following vowel. You will often see this in normal writing.

θα is the particle used to form the future in Modern Greek.

• απαντώ / απαντάω = I answer / I am answering
• θα απαντήσω = I will answer

So θα marks future time, and απαντήσω is the verb form used with it.

σου means to you.

Greek often uses a weak object pronoun before the verb where English might use a separate phrase:

• σου = to you / you (indirect object, singular)

So:

• θα σου απαντήσω = I will answer you / I will reply to you

Compare:

• μου απάντησε = he/she answered me
• σας απαντώ = I answer you (plural or formal singular)

Because object clitic pronouns in Greek usually come before the verb.

So Greek says:

• θα σου απαντήσω

not:

• θα απαντήσω σου

This is one of the patterns English speakers have to get used to. The short pronouns like μου, σου, του, μας, σας, τους usually appear before the verb.

After θα, Greek often uses a different verb form from the plain present.

Here:

• απαντώ / απαντάω = present: I answer / I am answering
• θα απαντήσω = future: I will answer

Many Greek verbs form the future with this kind of perfective stem. So learners should think of θα + verb as a unit, but also notice that the verb form itself may change.

Yes. They are forms of the same verb.

In dictionaries or everyday speech you may see:

• απαντώ
• απαντάω

Both mean to answer / to reply.
The future form here is:

• θα απαντήσω = I will answer

So don’t be confused by the different-looking stem. This is a normal part of Greek verb formation.

αργότερα means later.

It is the comparative adverb form of αργά (late), but in everyday use you can simply learn it as the normal word for later.

So:

• θα σου απαντήσω αργότερα = I’ll answer you later

Sometimes yes, but the meaning would shift slightly.

• αργότερα = later
• μετά = after / afterwards / then

In this sentence, αργότερα is the most natural choice because the speaker means at a later time.
Μετά could work in some contexts, but αργότερα sounds more precise here.

Because the sentence has two linked clauses:

1. Σήμερα δεν έχω ούτε καν δέκα λεπτά ελεύθερα
2. γι’ αυτό θα σου απαντήσω αργότερα

The comma helps separate the cause from the result:

• I don’t even have ten free minutes today, so I’ll answer you later.

This punctuation is natural in Greek, just as it is in English.

Greek word order is fairly flexible, but the original version is very natural.

For example, Greek could also say things like:

• Δεν έχω σήμερα ούτε καν δέκα λεπτά ελεύθερα...
• Θα σου απαντήσω αργότερα, γιατί σήμερα δεν έχω ούτε καν δέκα λεπτά ελεύθερα.

But the original sentence flows well because it presents:

1. the time frame: Σήμερα
2. the problem: δεν έχω ούτε καν δέκα λεπτά ελεύθερα
3. the consequence: γι’ αυτό θα σου απαντήσω αργότερα

So while the order is not completely rigid, this version is idiomatic and clear.