Μετά το κακάο δεν έχω τόση πείνα, αλλά έχω ακόμα λίγη δίψα.

Μετά means after, and here it is followed by το κακάο in the accusative.

This is a very common Greek pattern:

• μετά το μάθημα = after the lesson
• μετά τη δουλειά = after work
• μετά το φαγητό = after the meal

So Μετά το κακάο sets the time frame for the rest of the sentence: after the cocoa / hot chocolate.

Yes. Μετά το κακάο and μετά από το κακάο are both possible in Modern Greek.

• μετά το κακάο = a little shorter and more compact
• μετά από το κακάο = slightly fuller, also very natural

In everyday Greek, από after μετά is often optional.

In everyday Greek, κακάο can refer to:

• cocoa as a substance
• cocoa powder
• a cocoa drink, often basically hot chocolate depending on context

In this sentence, it most naturally sounds like the drink, because the speaker is talking about how they feel after having it.

Greek often expresses hunger and thirst with έχω + noun:

• έχω πείνα = literally I have hunger
• έχω δίψα = literally I have thirst

That is a normal Greek way to say:

• I’m hungry
• I’m thirsty

Greek also has adjective-based expressions such as είμαι πεινασμένος / πεινασμένη and είμαι διψασμένος / διψασμένη, but έχω πείνα / δίψα is very common and natural.

Δεν is the basic word for negating a verb. It means not.

So:

• έχω = I have
• δεν έχω = I do not have

In Greek, δεν normally goes directly before the finite verb, which is why you get δεν έχω.

They are the direct objects of έχω, so they are in the accusative.

A detail that can confuse learners is that for these nouns, the singular nominative and accusative forms look the same when there is no article:

• η πείνα / την πείνα
• η δίψα / τη(ν) δίψα

In the sentence, the article is omitted, so you simply see πείνα and δίψα.

Because πείνα and δίψα are feminine singular nouns, the words that modify them must match.

• τόση is the feminine singular form of τόσος
• λίγη is the feminine singular form of λίγος

So:

• τόση πείνα = that much / so much hunger
• λίγη δίψα = a little thirst

This is agreement: the modifier matches the gender and number of the noun.

Greek often leaves out the article with abstract or general states after έχω.

So these are very natural:

• έχω πείνα
• έχω δίψα
• έχω χρόνο

Using no article makes the statement general and neutral. Adding an article would usually make it sound more specific or more marked.

Here ακόμα means still.

So:

• έχω ακόμα λίγη δίψα = I still have a little thirst / I’m still a little thirsty

Yes, ακόμα and ακόμη are variants of the same word. Both are common. In other contexts, this word can also mean even or yet, but here the meaning is clearly still.

Those two are similar, but not identical.

• πολλή πείνα = a lot of hunger, very hungry
• τόση πείνα = that much / so much hunger

So δεν έχω τόση πείνα usually means something like I’m not that hungry or I’m not as hungry. It suggests a comparison with what you might expect, or with how hungry the speaker was before.

That makes it a good choice here: after the cocoa, the speaker is saying their hunger is reduced.

Αλλά means but.

It connects two contrasting ideas:

• δεν έχω τόση πείνα = I’m not that hungry
• έχω ακόμα λίγη δίψα = but I’m still a little thirsty

So it marks the contrast between less hunger and remaining thirst.

Greek word order is fairly flexible.

The given version:

• Μετά το κακάο δεν έχω τόση πείνα, αλλά έχω ακόμα λίγη δίψα.

is natural because it puts Μετά το κακάο first, setting the context right away.

You could also say:

• Δεν έχω τόση πείνα μετά το κακάο, αλλά έχω ακόμα λίγη δίψα.

That is also understandable and natural. The original just sounds a bit more organized in terms of information flow: first the context, then the comment.

A rough pronunciation is:

meh-TA to ka-KA-o then E-ho TO-si PEE-na, a-LA E-ho a-KO-ma LEE-yi THEEP-sa

A few useful notes:

• χ in έχω is not an English k. It is a throaty sound, like Spanish j in José or German ch in Bach.
• γ in λίγη is a soft sound here, close to a y-like sound.
• δ in δίψα is the voiced th sound, like in this, not the th of thin.
• Stress is shown by the accent marks: μετά, κακάο, έχω, τόση, πείνα, αλλά, ακόμα, λίγη, δίψα.