Γυρίζω το καπάκι του δοχείου για να το ανοίξω.

In this sentence, γυρίζω means I turn / I’m turning / I twist.

Greek present tense often covers both:

• I turn
• I am turning

So the exact English choice depends on context.

Also, γυρίζω can mean return / go back in other sentences, but here that meaning does not fit, because the object is το καπάκι (the lid).

Because Greek usually drops subject pronouns when the verb ending already shows the person.

γυρίζω clearly means I turn / I’m turning, so εγώ is not necessary.

You would add εγώ only for emphasis or contrast, for example:

• Εγώ γυρίζω το καπάκι, όχι εσύ. = I’m turning the lid, not you.

This is a noun phrase meaning the lid of the container.

Breakdown:

• το καπάκι = the lid
• του δοχείου = of the container

So του δοχείου is a genitive phrase showing possession or connection.

A very literal breakdown is:

• the lid
• of the container

Because it is in the genitive case.

Greek uses the genitive for meanings like:

• of
• belonging to
• associated with

So:

• το δοχείο = the container
• του δοχείου = of the container

This is why το καπάκι του δοχείου means the lid of the container.

Greek uses the definite article very often, more often than English in some situations.

Here the speaker is talking about a specific lid and a specific container, so Greek naturally says:

• το καπάκι
• του δοχείου

Literally, it is the lid of the container, not just lid of container.

για να introduces a purpose clause. Here it means:

• to
• in order to
• so that

So:

• για να το ανοίξω = to open it / in order to open it

In natural English, we often just say to open it, but Greek uses για να.

Because after να, Greek uses the subjunctive, not the ordinary indicative form.

So:

• ανοίγω = I open / I am opening as a normal main-clause verb
• να ανοίξω = that I open / to open in a subjunctive structure

In this sentence, ανοίξω is the correct form after για να.

Because Greek is showing aspect, not past time.

να ανοίξω is aorist subjunctive, and here it suggests a single complete action:

• to open it
• to get it open

That is natural after turning a lid: the goal is one completed result.

A present subjunctive form would suggest something more ongoing or repeated, which would sound less natural here.

Important point: aorist here does not mean past.

That το is a weak object pronoun meaning it.

So:

• να ανοίξω = to open
• να το ανοίξω = to open it

This το is not the article the. It is a pronoun.

Greek uses the same form το for:

• the neuter singular article: the
• the neuter singular object pronoun: it

You tell which one it is from the grammar of the sentence.

Because in Modern Greek, weak object pronouns usually come before a finite verb or subjunctive form.

So Greek says:

• να το ανοίξω

not:

• να ανοίξω το

This is normal Greek word order for clitic pronouns.

A useful contrast:

• να το ανοίξω = to open it
• Άνοιξέ το! = Open it!

With the imperative, the pronoun usually comes after the verb.

Grammatically, it could refer to either one, because both are neuter singular:

• το καπάκι = neuter singular
• το δοχείο = neuter singular

So the sentence can be a little ambiguous on its own.

In real life, the most likely meaning is:

• you turn the lid in order to open the container

But if you want to make that completely clear, Greek could say:

• Γυρίζω το καπάκι του δοχείου για να ανοίξω το δοχείο.

If you mean the lid itself, you could say:

• ...για να ανοίξω το καπάκι.

Yes. Greek word order is fairly flexible, though not completely free.

For example, you could also say:

• Για να το ανοίξω, γυρίζω το καπάκι του δοχείου.

That means the same thing, but now the purpose comes first:

• To open it, I turn the lid of the container.

What usually stays fixed is the position of the weak pronoun:

• να το ανοίξω, not usually να ανοίξω το

No. It is a good, natural verb here, but other verbs are also possible depending on the exact meaning.

For example:

• γυρίζω = turn
• στρίβω = twist/turn
• ξεβιδώνω = unscrew

If the idea is specifically that the lid is screw-on and you are removing it by twisting, ξεβιδώνω may be even more precise.

But γυρίζω το καπάκι is perfectly understandable and natural.