Ο γείτονας έγινε πλούσιος.

Ο is the masculine singular nominative form of the.

It matches γείτονας, which is a masculine singular noun here, so ο γείτονας means the neighbor. In this sentence, ο γείτονας is the subject.

Because γείτονας is the nominative singular form, and the subject of the sentence has to be in the nominative.

Here, the neighbor is the one doing the action of becoming, so Greek uses ο γείτονας.
By contrast, γείτονα is typically the accusative singular, as in:

Βλέπω τον γείτονα. = I see the neighbor.

Έγινε is the aorist form of γίνομαι.

In this sentence, it means became or got:
Ο γείτονας έγινε πλούσιος. = The neighbor became rich / got rich.

The aorist is the normal Greek past tense for a completed event.

Because γίνομαι is an irregular verb in the past.

Its aorist stem changes, so instead of something fully predictable, you get forms like:

• έγινα = I became
• έγινες = you became
• έγινε = he/she/it became

So έγινε is just the normal 3rd person singular past form of γίνομαι.

This is a very common learner question. Γίνομαι is one of those Greek verbs that uses middle/passive-type endings but has an active meaning.

So even though it may look passive in form, γίνομαι means things like:

• become
• happen
• be made / be done in some contexts

Here, έγινε πλούσιος definitely means he became rich, not he was become rich or anything passive like that.

Because πλούσιος is a predicate adjective after έγινε, and it has to agree with the subject.

The subject is ο γείτονας, which is:

• masculine
• singular
• nominative

So the adjective is also:

• masculine
• singular
• nominative

That is why you get πλούσιος.

Because Greek adjectives must agree with the noun they describe or refer back to.

Here the subject is masculine singular, so:

• masculine: πλούσιος
• feminine: πλούσια
• neuter: πλούσιο

So:

• Ο γείτονας έγινε πλούσιος. = The male neighbor became rich.
• Η γειτόνισσα έγινε πλούσια. = The female neighbor became rich.

It is an adjective here, meaning rich.

It describes the state that the neighbor came to be in. So the structure is:

• Ο γείτονας = subject
• έγινε = became
• πλούσιος = rich

So this is like English He became rich, where rich is also an adjective.

Yes. That is a very natural translation.

Greek έγινε πλούσιος can be understood as:

• became rich
• got rich

The exact English wording depends on style, but the Greek meaning is the same.

Yes. Greek word order is more flexible than English.

The neutral order here is:

Ο γείτονας έγινε πλούσιος.

But you could also say:

Πλούσιος έγινε ο γείτονας.

That still means the same thing, but now πλούσιος is more emphasized, as if you were highlighting the result: Rich is what the neighbor became.

A rough pronunciation is:

o YEE-toh-nas EH-yee-neh PLOO-see-os

A few helpful points:

• γεί- sounds roughly like yee-
• έγινε has the stress on the first syllable: EH-yee-neh
• πλούσιος has the stress on πλού-

The written accents show the stressed syllables:

• γείτονας
• έγινε
• πλούσιος

In this sentence, yes, it refers to a masculine noun phrase.

For a female neighbor, Greek would normally use:

η γειτόνισσα

So:

• Ο γείτονας έγινε πλούσιος. = The male neighbor became rich.
• Η γειτόνισσα έγινε πλούσια. = The female neighbor became rich.