Άνοιξε το ντουλάπι και πάρε ένα ποτήρι.

Here it is an imperative: Open.

That said, άνοιξε can also be the 3rd person singular aorist of ανοίγω, meaning he/she/it opened. Greek allows this ambiguity in form.

So how do you know which one it is here?

• The sentence is clearly giving instructions.
• It is followed by another imperative, πάρε.
• The whole structure sounds like a command sequence: Open the cupboard and take a glass.

So in this sentence, Άνοιξε is definitely understood as Open.

Both are 2nd person singular imperative forms, used to tell one person what to do.

More specifically, they are aorist imperatives:

• Άνοιξε = aorist imperative of ανοίγω
• πάρε = aorist imperative of παίρνω

In Modern Greek, the aorist imperative is very common for a single, complete action:

• open it
• take one

That matches this sentence perfectly.

Because the speaker is asking for two one-time, completed actions:

• open the cupboard
• take a glass

The aorist imperative is the normal choice for that.

If you used the present imperative, it would suggest something more like:

• repeated action
• ongoing action
• habitual behavior
• emphasis on the process rather than the completed act

So:

• Άνοιξε = open it once
• πάρε = take one

That is why these forms sound natural here.

Because παίρνω has an irregular aorist stem.

Its basic forms are:

• present: παίρνω = I take
• aorist: πήρα = I took
• aorist imperative: πάρε = take

So the verb does not build all its forms from the exact same visible stem. This is common in Greek: many verbs have one stem in the present and a different one in the aorist.

So πάρε is something you should learn as part of the verb’s principal forms, not something you can always guess mechanically from παίρνω.

Because Greek usually does not need to state the subject pronoun.

The imperative form itself already tells you that the speaker is addressing you:

• Άνοιξε = you open
• πάρε = you take

Adding εσύ would usually sound emphatic, contrastive, or emotionally marked:

• Εσύ άνοιξε το ντουλάπι... would feel like you open the cupboard..., as opposed to someone else.

So the version without a pronoun is the normal one.

This is the difference between the definite and indefinite article.

• το ντουλάπι = the cupboard/cabinet
• ένα ποτήρι = a glass

So the cupboard is treated as specific/known to the listener, while the glass is not specified: any one glass will do.

Both nouns are neuter singular, which is why you see:

• το with ντουλάπι
• ένα with ποτήρι

They are both direct objects, so they are in the accusative case.

• το ντουλάπι = object of Άνοιξε
• ένα ποτήρι = object of πάρε

A useful detail: with neuter singular nouns, the nominative and accusative forms are often the same in appearance. So even though these nouns are accusative here, they look the same as dictionary-style forms.

That is why you do not see an obvious ending change.

You would use the plural/polite imperative:

Ανοίξτε το ντουλάπι και πάρτε ένα ποτήρι.

So:

• singular/informal: Άνοιξε ... και πάρε ...
• plural or polite singular: Ανοίξτε ... και πάρτε ...

Greek uses the plural form both for:

• talking to more than one person
• speaking politely to one person

Yes, Greek word order is fairly flexible, but the original order is very natural and neutral:

Άνοιξε το ντουλάπι και πάρε ένα ποτήρι.

This is basically:

• verb + object
• και
• verb + object

You can change the order, but that may change the emphasis or the sequence:

• Πάρε ένα ποτήρι και άνοιξε το ντουλάπι.
  This changes the order of the actions.

• Άνοιξε και το ντουλάπι.
  This can mean open the cupboard too, where και means also rather than simply linking two actions.

So yes, the order can change, but the original sentence is the straightforward version.

A rough pronunciation guide is:

• Άνοιξε = AH-nee-kseh
• το = toh
• ντουλάπι = doo-LA-pee
• και = keh (often closer to kay/keh depending on speech)
• πάρε = PA-reh
• ένα = EH-na
• ποτήρι = po-TEE-ree

A few helpful notes:

• οι in Άνοιξε is pronounced ee, not like English oi.
• ντ at the beginning of ντουλάπι sounds like d.
• The accent mark shows the stressed syllable:
  • Άνοιξε
  • ντουλάπι
  • πάρε
  • ποτήρι

It is very close, but the exact English translation depends on context.

ντουλάπι often means:

• cupboard
• cabinet

So in a kitchen, το ντουλάπι might be the cupboard or the cabinet.

It is a general storage-unit word, and English may choose different translations depending on the room or situation.