Η γιατρός κοίταξε το μέτωπό της και μετά το πηγούνι της.

Because γιατρός is one of those Greek profession nouns that can refer to either a man or a woman. The article shows the gender here:

• ο γιατρός = the (male) doctor
• η γιατρός = the (female) doctor

So in this sentence, Η γιατρός tells you the doctor is female.

Also, although some speakers may use γιατρίνα, the standard neutral form in many contexts is still η γιατρός for a woman.

Κοίταξε is the aorist tense, third person singular, from κοιτάζω / κοιτάω.

Here it means something like:

• she looked at
• she examined

The aorist presents the action as a single completed event in the past.

Compare:

• κοίταξε = looked / took a look at
• κοίταζε = was looking at / kept looking at

So this sentence describes a sequence of completed actions.

Because κοιτάζω in Greek normally takes a direct object, not a preposition.

So Greek says:

• κοίταξε το μέτωπο
  literally: looked the forehead

But natural English needs:

• looked at the forehead

This is very common when learning Greek: the verb pattern is different from English, even though the meaning is the same.

Here της means her.

More specifically, it is the genitive weak pronoun used to show possession:

• το μέτωπό της = her forehead
• το πηγούνι της = her chin

So της is functioning like an English possessive.

Be aware that της can also mean to her or of her in other contexts, but here the meaning is clearly possessive.

This is because of a Greek stress rule involving enclitics like της.

The basic word is:

• μέτωπο

When a word stressed on the third-from-last syllable is followed by an enclitic such as της, Greek often adds a second written accent:

• το μέτωπό της

This helps show the correct pronunciation pattern.

But πηγούνι is already stressed closer to the end of the word, so no extra accent is needed:

• το πηγούνι της

So the difference is due to stress placement, not a difference in meaning.

They are in the accusative singular because they are the direct objects of κοίταξε.

The doctor looked at:

• το μέτωπό της
• το πηγούνι της

Both nouns are neuter singular, and with many neuter nouns the nominative and accusative forms look the same. So you identify the case mainly from their role in the sentence.

Greek often repeats the article with each noun in a series, especially when the nouns are being treated as separate items:

• το μέτωπό της και το πηγούνι της

This is very natural Greek.

English often avoids repeating the, but Greek is more comfortable repeating it. The repeated article makes the structure clearer and more balanced.

Repeating της makes it clear and natural that both body parts belong to the same person:

• το μέτωπό της και το πηγούνι της

Greek often repeats possessive pronouns in this kind of structure, especially with body parts.

You may sometimes see less repetition in other sentences, but here the repetition sounds very normal and explicit.

Here μετά means then / afterwards.

So:

• και μετά = and then

Greek μετά can also mean after, but that happens when it is followed by a noun phrase:

• μετά το μάθημα = after the lesson

In this sentence, it stands on its own as an adverb, so the meaning is then.

Yes. In this context, because the subject is a doctor, κοίταξε can naturally suggest examined or checked.

So depending on context, the sentence could feel like:

• The doctor looked at her forehead and then her chin
• The doctor examined her forehead and then her chin

The Greek verb itself is still κοίταξε; the more specific nuance comes from the situation.

Grammatically, της just means her, so by itself it does not automatically tell you whether it is the doctor’s own body parts or another female person’s.

In real use, the context decides.

However, in an ordinary real-world reading, a sentence like this usually suggests that the female doctor looked at another woman’s forehead and chin, not her own. That is because of the situation described.

So the grammar gives her, and the wider context tells you exactly whose her it is.