Mater puellam monet ut ante lararium taceat et flores recte ponat.

Because puellam is the direct object of monet.

The verb moneō, monēre can mean warn, advise, remind, or instruct, and the person being warned or advised is put in the accusative:

• Mater puellam monet = The mother advises/warns the girl

So puellam is accusative singular of puella.

This is a very common Latin pattern:

moneō + accusative person + ut + subjunctive

It means something like:

• advise someone to do something
• warn someone to do something
• tell someone that they should do something

So in this sentence:

• Mater puellam monet ut ... = The mother advises the girl to...

Latin often uses ut plus the subjunctive where English might use an infinitive such as to be silent or to place.

Here ut introduces a subordinate clause of command, advice, or urging.

After verbs like moneō, hortor, imperō, and similar verbs, Latin often uses:

• ut
  • subjunctive for a positive command or instruction
• nē
  • subjunctive for a negative one

So:

• monet ut taceat = advises her to be silent
• if it were negative, you might expect monet nē loquātur = advises her not to speak

In this sentence, ut does not mean so that. It means something more like that or to after monet.

They are subjunctive because they are inside the ut clause after monet.

This is a standard use of the subjunctive in a clause expressing what someone is urged, advised, or told to do.

So:

• taceat = that she be silent / that she should be silent
• ponat = that she place / that she should place

These are both present subjunctive, active, third person singular.

Because the main verb is also present: monet.

In Latin, a present main verb is normally followed by the present subjunctive in this kind of clause. This follows the sequence of tenses.

So:

• monet ut taceat = present main verb + present subjunctive

If the main verb were past, Latin would usually shift to the imperfect subjunctive:

• monuit ut taceret = she advised her to be silent

The understood subject is the girl, even though Latin does not repeat puella inside the clause.

So the sense is:

• Mother advises the girl that she should be silent and place the flowers properly

Latin often leaves the subject unstated when it is clear from context. Here, the girl is the natural person being told what to do.

Because both verbs belong to the same ut clause.

The structure is:

• ut taceat et flores recte ponat

That means:

• that she be silent and place the flowers properly

Latin does not need to repeat ut before the second verb when both verbs are parallel and part of the same clause.

Because flores is the direct object of ponat.

The verb pōnō, pōnere means put, place, or set, and what is being placed goes into the accusative.

So:

• flores ponat = she should place the flowers

flores is accusative plural of flōs.

Recte is an adverb modifying ponat.

It means properly, correctly, or in the right way.

So:

• flores recte ponat = she should place the flowers properly

It does not describe the flowers themselves; it describes the manner of placing them.

Because ante is a preposition that takes the accusative.

So:

• ante lararium = before/in front of the shrine

Even though lararium looks the same in the nominative and accusative singular, here it is accusative because ante requires it.

Lararium is a neuter second-declension noun.

Its basic form is:

• nominative singular: lararium
• genitive singular: larariī

Because it is neuter, the nominative and accusative singular are the same in form:

• lararium

In this sentence, it is accusative singular because it follows ante.

Taceat comes from taceō, tacēre, meaning be silent, keep quiet, or say nothing.

In this sentence it is not just describing what she is doing; it expresses what she is being told to do:

• that she should be silent

So it has a slightly command-like or instructed sense because of the ut clause after monet.

Latin word order is much more flexible than English word order because Latin shows grammatical relationships through endings, not mainly through position.

English depends heavily on order:

• The mother advises the girl

Latin can move words around more freely:

• Mater puellam monet
• Puellam mater monet
• Monet mater puellam

All of these can mean the same basic thing, though the emphasis may change.

In your sentence, the verbs of the subordinate clause come near the end:

• ut ante lararium taceat et flores recte ponat

That is very natural Latin style.

Yes. Moneō has a wider range than just English warn.

Depending on context, it can mean:

• warn
• advise
• remind
• instruct

In this sentence, because the mother is telling the girl how to behave and what to do, advises or instructs may fit especially well.

So learners should not assume moneō always means a warning about danger.