Η αστυνομία βρήκε ένα ίχνος.

Η is the definite article in Greek, here meaning the.

• η αστυνομία = the police
• Greek uses articles very often, including with subjects of sentences.

A few useful details:

• η is the feminine singular nominative form of the
• It is pronounced i

So Η αστυνομία literally is the police.

In this sentence, αστυνομία is grammatically singular in Greek.

That is one of the biggest differences from English:

• English: The police found... often takes a plural verb
• Greek: Η αστυνομία βρήκε... uses a singular verb

So:

• η αστυνομία = the police, the police force
• βρήκε = found (3rd person singular)

If you wanted to talk about police officers as people, Greek often uses:

• οι αστυνομικοί = the police officers / the cops

Yes, αστυνομία is a feminine noun.

However, the verb βρήκε is not feminine. Greek verbs do not change for grammatical gender the way adjectives or articles do. They change mainly for:

• person
• number
• tense/aspect

So βρήκε simply means he/she/it found or found with a 3rd-person singular subject.

In this sentence, the subject is η αστυνομία, so the meaning is:

• The police found...

The femininity of αστυνομία affects the article (η), but not the verb form.

Βρήκε is the aorist form of βρίσκω (to find).

Here it corresponds to the English simple past:

• βρίσκω = I find / I am finding
• βρήκε = he/she/it found

So in this sentence:

• Η αστυνομία βρήκε ένα ίχνος.
• The police found a trace/clue.

The aorist usually presents the action as a completed event.

Because the sentence refers to a completed past action.

• βρίσκει = finds / is finding (present)
• βρήκε = found (aorist/past)

So compare:

• Η αστυνομία βρίσκει ένα ίχνος. = The police finds / is finding a trace
  (present; much less natural in many contexts)
• Η αστυνομία βρήκε ένα ίχνος. = The police found a trace
  (past; natural here)

Because ίχνος is a neuter singular noun, and ένα is the neuter singular indefinite article, meaning a / an.

So:

• ένα = a / an for neuter nouns
• ίχνος = a neuter noun

Useful article set:

• ένας = masculine
• μία / μια = feminine
• ένα = neuter

So ένα ίχνος means a trace / a clue.

It is in the accusative singular, because it is the direct object of the verb βρήκε.

The police did the action, and a trace is what they found.

So:

• η αστυνομία = subject
• βρήκε = verb
• ένα ίχνος = direct object

A useful thing to know: for many neuter nouns, the nominative and accusative forms are the same in the singular. So ίχνος looks the same here.

Because for this noun, the singular nominative and accusative are the same form: ίχνος.

So you get:

• το ίχνος = the trace
• ένα ίχνος = a trace

Even though its grammatical role changes, the form stays the same here.

This is very common with neuter nouns in Greek.

Not always exactly. Ίχνος more literally means something like:

• trace
• track
• mark
• sign

In a police context, it can naturally be understood as:

• a trace
• a clue
• evidence/sign of someone or something

So depending on context, English may translate it in slightly different ways.

No, Greek word order is fairly flexible, although subject–verb–object is the most neutral order here:

• Η αστυνομία βρήκε ένα ίχνος.

You may also see other orders for emphasis, for example:

• Ένα ίχνος βρήκε η αστυνομία.
  = It was a trace that the police found
• Βρήκε ένα ίχνος η αστυνομία.
  = also possible, with different emphasis or style

Because Greek uses articles and case more than English does, word order can move around more easily.

Yes. Greek often drops subject pronouns and sometimes even subject nouns when the meaning is clear from context.

So you could say:

• Βρήκε ένα ίχνος.

This means:

• He/she/it found a trace, or
• The police found a trace, if the context already makes that clear

In your full sentence, η αστυνομία is included to make the subject explicit.

A simple pronunciation guide is:

• i astino-MEE-a VREE-ke E-na IH-hnos

A slightly more careful breakdown:

• Η = i
• αστυνομία = astinomía
• βρήκε = vríke
• ένα = éna
• ίχνος = íchnos

A few notes:

• βρ sounds like vr
• χ in ίχνος is not an English k sound; it is a rough h/ch sound
• The written accents show which syllable is stressed:
  • αστυνομία
  • βρήκε
  • ένα
  • ίχνος

The dictionary forms are:

• η αστυνομία = the police
• βρίσκω = to find
• το ίχνος = the trace / track / clue

This is useful because the sentence uses an inflected verb form:

• dictionary form: βρίσκω
• sentence form: βρήκε

So when learning vocabulary, you would usually memorize:

• η αστυνομία
• βρίσκω
• το ίχνος