Δεν γίνεται να έρθω τώρα, δουλεύω.

Here γίνεται comes from γίνομαι, which often means to happen, to become, or to be possible.

In Δεν γίνεται να έρθω τώρα, it is being used impersonally. That means Greek is not really saying he/she/it happens in a normal literal way. The whole expression Δεν γίνεται να... means something like:

• It’s not possible to...
• There’s no way to...
• I can’t really... (depending on context)

So γίνεται is singular because this is a fixed impersonal pattern.

Because Modern Greek does not use an infinitive the way English does.

Where English says:

• I can’t come
• It’s impossible to come

Greek usually uses να + verb instead. So:

• να έρθω = literally something like that I come, but in natural English it often corresponds to to come or come

This is one of the most important differences between English and Greek structure.

Έρθω is the 1st person singular form, so it means I come in this kind of να clause.

More specifically, it is the aorist subjunctive form of έρχομαι.

That sounds technical, but the important idea is this:

• έρχομαι = I come / I am coming
• να έρθω = to come / that I come, usually as one complete action

So in this sentence, Greek is talking about the single act of coming now, not a repeated or ongoing action.

Because να έρθω treats the action as one whole event: to come now.

That is exactly what fits this sentence. The speaker means:

• I can’t come right now

If you used να έρχομαι, it would sound more like:

• to be coming
• to come regularly
• to keep coming

That does not fit well here. So να έρθω is the natural choice.

Because δεν is negating the main verb γίνεται.

So the structure is:

• Δεν γίνεται = it’s not possible
• να έρθω = for me to come

You use μη(ν) to negate the να-clause itself. For example:

• να μην έρθω = not to come

So these are different:

• Δεν γίνεται να έρθω = It’s not possible for me to come
• Δεν γίνεται να μην έρθω = It’s not possible for me not to come

That contrast is very useful to understand.

Because Greek usually does not need subject pronouns when the verb ending already shows who the subject is.

Here:

• έρθω already shows I
• δουλεύω also already shows I

So Greek naturally leaves out εγώ.

You could add εγώ, but then it would sound more emphatic, like:

• I can’t come right now, I’m working

In normal speech, leaving it out is more natural.

It can mean either one, depending on context.

The Greek present tense often covers both:

• I work
• I am working

In this sentence, because of τώρα and the situation, the most natural meaning is:

• I’m working

So δουλεύω here is best understood as a present, current activity.

A comma is very natural here in Greek, especially in spoken-style writing.

The second clause δουλεύω explains the reason:

• Δεν γίνεται να έρθω τώρα, δουλεύω.
• I can’t come now, I’m working.

Greek often allows this kind of simple clause linking without an explicit because.

You could also say:

• Δεν γίνεται να έρθω τώρα γιατί δουλεύω.

That is also correct and makes the cause more explicit.

Both are common, but they are not exactly the same.

• Δεν μπορώ να έρθω τώρα = I can’t come now
• Δεν γίνεται να έρθω τώρα = It’s not possible for me to come now / There’s no way I can come now

Δεν μπορώ focuses more directly on ability / possibility for the speaker.

Δεν γίνεται often sounds a bit more like:

• the circumstances do not allow it
• it just won’t work
• it’s not feasible

In everyday speech, Δεν γίνεται can sound slightly more colloquial and expressive.

It is neutral to informal spoken Greek, and very natural.

It sounds like something someone would say in everyday conversation.

A more formal version might be:

• Δεν είναι δυνατό να έρθω αυτή τη στιγμή, εργάζομαι.

That is more formal and less conversational.

So the original sentence is good, natural everyday Greek.

Yes. Greek word order is more flexible than English word order.

The original:

• Δεν γίνεται να έρθω τώρα, δουλεύω.

is perfectly natural.

But you could also hear:

• Τώρα δεν γίνεται να έρθω, δουλεύω.
• Δεν γίνεται τώρα να έρθω, δουλεύω.

These all mean roughly the same thing, but the emphasis shifts a little:

• τώρα earlier in the sentence gives more focus to right now
• να έρθω τώρα keeps the idea of come now closely together

So the original order is natural and clear, but alternatives are possible.