Mater dicit librum in tablino positum esse et flores ante lararium a filia positos esse.

Because Latin often uses indirect statement instead of a that-clause.

After a verb like dicit (says), Latin commonly puts:

• the subject of the reported statement in the accusative
• the verb of the reported statement in the infinitive

So:

Mater dicit librum positum esse
literally = Mother says the book to have been placed
natural English = Mother says that the book has been placed

This is one of the most important Latin constructions to learn.

In an indirect statement, the subject of the infinitive goes into the accusative.

So in:

librum in tablino positum esse

the word librum is not the direct object of positum esse. It is actually the subject of that infinitive phrase, but Latin puts that subject in the accusative because the whole clause depends on dicit.

You can compare:

• direct statement: liber in tablino positus est = the book has been placed in the study
• indirect statement: mater dicit librum in tablino positum esse = mother says that the book has been placed in the study

Notice how liber becomes librum.

Positum esse is the perfect passive infinitive of pono, ponere, posui, positum (to place, put).

It is made from:

• the perfect passive participle: positum
• plus esse

So:

• positum esse = to have been placed
• in smoother English here: has been placed or was placed

The same pattern appears again in:

• positos esse = to have been placed for a plural masculine noun

Because the participle must agree with the noun it goes with in:

• gender
• number
• case

So:

• librum = masculine singular accusative
  → positum

• flores = masculine plural accusative
  → positos

Even though positum/positos is part of the verb phrase positum esse / positos esse, it is still a participle and therefore agrees like an adjective.

Because the two prepositions work differently.

• in with the ablative usually means in / on a place
  so in tablino = in the study

• ante takes the accusative
  so ante lararium = in front of the household shrine

A very common thing for learners to remember is:

• in + ablative = in somewhere
• in + accusative = into somewhere

Here it is in tablino, so it means location, not motion.

Because with a passive verb, the personal agent is often expressed by a/ab + ablative.

So:

• a filia = by the daughter

This tells you who did the action of placing the flowers.

A useful contrast:

• a filia = by the daughter after a passive verb
• if Latin were simply saying the daughter placed the flowers, then filia would be nominative

Both a and ab mean the same thing here.

Before a consonant, Latin often uses a, though ab can also appear.
Before a vowel, ab is more usual.

Since filia begins with f, a filia is perfectly normal.

Because there are really two parallel indirect statements joined by et:

• librum in tablino positum esse
• flores ante lararium a filia positos esse

Each one needs its own infinitive, so esse is repeated.

This makes the structure very clear:

• Mother says that the book has been placed...
• and that the flowers have been placed...

Because flos, floris (flower) is a masculine noun in Latin.

Its plural accusative is flores, so the participle must also be masculine plural accusative:

• flores ... positos esse

If the noun were feminine plural accusative, then positas would be right, but not here.

Yes, Latin word order is much freer than English word order.

This sentence separates nouns from their participles:

• librum ... positum esse
• flores ... positos esse

and places the location phrases in between:

• in tablino
• ante lararium

That is normal Latin style. The endings tell you which words belong together.

So a learner should look for:

• librum ↔ positum
• flores ↔ positos

rather than expecting the words to stay next to each other the way they usually would in English.