Pater dicit se post undeviginti dies domum rediturum esse.

Because se is the reflexive pronoun, and it refers back to the subject of the main verb, pater.

So in this sentence:

• Pater dicit = Father says
• se ... rediturum esse = that he will return

The he in English is the same person as father, so Latin uses se.

A helpful contrast:

• Pater dicit se venturum esse = Father says that he will come
  
  • se = father himself
• Pater dicit eum venturum esse = Father says that he will come
  
  • eum = some other male person, not father

So se is important because it shows that father is talking about himself.

Because after verbs of saying, thinking, knowing, perceiving, and similar verbs, Latin often uses an indirect statement construction rather than a finite clause with that.

English says:

• Father says that he will return home

Latin usually does this with:

• subject accusative + infinitive

So:

• se = the subject of the indirect statement, in the accusative
• rediturum esse = infinitive meaning will return

This is the standard Latin pattern:

• dicit
  • accusative
    • infinitive

So Pater dicit se ... rediturum esse literally works like:

• Father says himself to be about to return...

That sounds strange in English, but it is normal Latin.

Rediturum is the future active participle of redeo (to return).

Its basic meaning is:

• about to return
• going to return

In this sentence it is:

• masculine
• singular
• accusative

because it agrees with se, which is also accusative singular and refers to pater.

So:

• se rediturum esse = that he is going to return / that he will return

If the subject were feminine, you would get redituram esse.

Because the normal future infinitive in Latin is made with:

• future participle + esse

So:

• rediturus esse = to be about to return
• in accusative agreement with se: rediturum esse

This whole phrase functions as the infinitive in the indirect statement.

Without esse, the grammar would be incomplete in normal prose.

So the structure is:

• se = accusative subject
• rediturum esse = future infinitive

Together:

• se rediturum esse = that he will return

Because domum is one of the special words in Latin that can show motion toward place without a preposition.

So:

• domum = homeward / home
• domum redire = to return home

This is similar to how Latin treats names of cities, small islands, and a few special nouns such as:

• domus = home
• rus = countryside
• humus = ground

Examples:

• Romam it = he goes to Rome
• domum venit = he comes home
• domum redit = he returns home

So domum is an accusative of motion toward place, and no preposition is needed.

Because post takes the accusative case, not the ablative.

So:

• post
  • accusative = after
• dies here is accusative plural

This can be confusing because dies looks the same in nominative plural and accusative plural.

So in this sentence:

• post undeviginti dies = after nineteen days / in nineteen days

If Latin wanted to use the ablative, it would need a different construction, not post.

Undeviginti means nineteen.

It is built in the Roman subtractive style:

• unus de viginti in effect = one from twenty
• so undeviginti = nineteen

Latin numbers from 18 and 19 are often formed this way:

• duodeviginti = eighteen
• undeviginti = nineteen

So although English learners may expect a form more like nine-teen, Latin often expresses it as one before twenty.

It can naturally be understood as either, depending on context, and English often chooses in nineteen days in this kind of sentence.

Literally:

• post undeviginti dies = after nineteen days

But idiomatically in context it may mean:

• he will return in nineteen days
• that is, nineteen days from now

So the Latin expression marks a time point after a span of nineteen days.

The future infinitive shows action that is future relative to the main verb.

So:

• dicit = he says now
• rediturum esse = that he will return later

The return has not happened yet at the time of the saying.

This is exactly why the future infinitive is used: it expresses future time inside an indirect statement.

A useful comparison:

• dicit se redire = he says that he is returning / returns
• dicit se rediisse = he says that he returned / has returned
• dicit se rediturum esse = he says that he will return

Not really in the ordinary sense.

In the indirect statement construction, se is the subject of the infinitive rediturum esse, but because Latin puts the subject of an indirect statement in the accusative, it can look like an object.

So grammatically:

• main verb: dicit
• indirect statement:
  • subject: se (accusative)
  • verb: rediturum esse (infinitive)

So se belongs with rediturum esse, not directly as a simple object of dicit.

Latin word order is much freer than English word order, because Latin uses case endings to show grammatical function.

Putting rediturum esse at the end is very natural in Latin, especially in prose. It lets the sentence build toward the main idea of the indirect statement.

So the sentence moves like this:

• Pater dicit = the main statement begins
• se = who is involved in the indirect statement
• post undeviginti dies = when
• domum = where to
• rediturum esse = the key action, saved for the end

This kind of ending often sounds very natural and elegant in Latin.

In standard classical Latin, after dicit, the normal way to express that he will return is the accusative and infinitive construction, not a clause with quod or ut.

So:

• Pater dicit se ... rediturum esse = standard classical Latin

A finite clause with quod is possible in some later or less classical usage, but it is not the normal construction you are expected to learn first.

And ut would not be used here for ordinary indirect statement.

So this sentence is using the standard classical pattern.

The word comes from redeo, redire, redii/redivi, reditum, meaning to go back, return.

The future active participle is:

• rediturus, reditura, rediturum

In this sentence you see the accusative masculine singular form:

• rediturum

because it agrees with se, referring to pater.