Post paucos dies familia ex Italia ad Graeciam navigat.

Because post is a preposition that takes the accusative case when it means after.

So:

• post = after
• paucos dies = a few days in the accusative

That is why both words are in the accusative:

• paucos = accusative plural masculine
• dies = accusative plural

Latin often uses:

• post + accusative = after ...

So post paucos dies means after a few days.

Paucos is the adjective few agreeing with dies.

Since dies here is:

• plural
• masculine
• accusative

the adjective must match it:

• pauci = few
• paucos = few, in the masculine accusative plural

This is a basic Latin rule: adjectives agree with the nouns they describe in gender, number, and case.

So:

• dies = days
• paucos dies = a few days

Dies belongs to the fifth declension, and some of its forms look identical.

Here, dies can look like:

• nominative plural
• accusative plural

You know it is accusative plural here because:

1. it follows post, which takes the accusative
2. it is modified by paucos, which is clearly accusative plural

So grammar tells you the case, even though the noun form itself looks unchanged.

In Latin, familia is a singular noun, just like family in English.

So Latin treats it as one unit:

• familia navigat = the family sails / the family travels

Even though a family contains several people, the noun itself is singular, so the verb is singular too:

• navigat = he/she/it sails

This matches familia, which is singular.

Latin has no definite article and no indefinite article.

So Latin does not have separate words for:

• the
• a / an

That means familia can mean, depending on context:

• family
• the family
• a family

English has to add an article, but Latin usually does not.

Because Latin uses different prepositions, with different cases, for movement away from and movement toward.

ex Italia

• ex = out of, from
• ex takes the ablative
• so Italia here is ablative: from Italy

ad Graeciam

• ad = to, toward
• ad takes the accusative
• so Graeciam is accusative: to Greece

So the pattern is:

• ex + ablative = from
• ad + accusative = to

Because ad takes the accusative case.

The basic noun is Graecia = Greece, but after ad it changes form:

• nominative: Graecia
• accusative: Graeciam

So:

• ad Graeciam = to Greece

This is the normal first-declension accusative singular ending: -am.

It does change, but in ordinary writing without macrons, you often cannot see the difference clearly.

The word is first declension:

• nominative: Italia
• ablative: Italiā

After ex, the noun must be ablative, so the full form is Italiā.

Many beginner texts omit macrons, so both are written simply as Italia.
If macrons were shown, the phrase would be:

• ex Italiā

So yes, the case does change; it is just not always visible in spelling without vowel marks.

Navigat comes from navigo, navigare and means:

• sails
• travels by ship
• sometimes more generally voyages

In this sentence, because the family is going from Italy to Greece, navigat suggests travel by sea:

• the family sails from Italy to Greece

So it is more specific than simply goes.

Navigat is the third person singular present active indicative:

• navigat = he/she/it sails

Since familia is singular, navigat matches it.

If the sentence’s meaning has been translated into English as a present tense, then it is just a normal present. In some stories, Latin also uses the present tense to narrate past events vividly, but in a beginner sentence like this, it is usually best understood simply as:

• the family sails
• or the family is sailing

depending on the English translation style.

Latin word order is more flexible than English word order because the endings show each word’s role.

English usually prefers something like:

• The family sails from Italy to Greece after a few days.

But Latin can put the time expression first:

• Post paucos dies familia ex Italia ad Graeciam navigat.

That opening phrase, post paucos dies, sets the scene: after a few days.

So the sentence order is natural Latin, even though it does not match standard English order exactly.

Sometimes yes, but this depends on the kind of place name.

With names of cities, small islands, and a few special words like domus, Latin often uses no preposition for motion toward or motion from.

But Italia and Graecia are larger regions/countries, so Latin normally uses prepositions:

• ex Italia = from Italy
• ad Graeciam = to Greece

So in this sentence, the prepositions are exactly what you would expect.

Here post is temporal and means after.

But post can also mean behind in a spatial sense, depending on context.

For example:

• temporal: post paucos dies = after a few days
• spatial: post villam = behind the house

In your sentence, because dies means days, the meaning must be temporal: after.