Mater infantem monet ne aquam e catino effundat.

Because infantem is the direct object of monet.

The verb moneō, monēre means to warn, advise, or remind. In this sentence, the mother is warning the child, so the child is the person directly affected by the verb. That makes infantem accusative.

So:

• mater = the mother, nominative, the subject
• infantem = the child, accusative, the object of monet

Here monet means warns or advises.

It comes from moneō, monēre. This verb can have a range of meanings depending on context, including:

• warn
• advise
• remind

In this sentence, the sense is clearly warns:

• Mater infantem monet = The mother warns the child

Then the rest of the sentence explains what the warning is about.

Because ne is the usual word for that ... not in a clause expressing a negative command, warning, or instruction.

After verbs like monet, Latin often uses a clause with ut or ne:

• ut = that
• ne = that ... not

So:

• monet ne effundat = warns [him/her] not to spill

This is different from non.
Non usually just negates a word or statement directly, but ne is the normal choice in this kind of subordinate clause.

Because after monet with ne, Latin uses the subjunctive in the subordinate clause.

So ne aquam e catino effundat is not a simple statement like he spills the water. It is the content of the warning:

• she warns him not to spill the water

That kind of clause regularly takes the subjunctive in Latin.

Here effundat is present subjunctive, from effundō, effundere.

The subject is understood to be the child—that is, infantem.

Even though infantem is accusative in the main clause because it depends on monet, it is also the person who would do the spilling in the subordinate clause.

So the sense is:

• The mother warns the child that the child should not spill the water

English usually says this more naturally as:

• The mother warns the child not to spill the water

Latin does not need to repeat the subject here.

Because aquam is the direct object of effundat.

The verb effundere means to pour out or to spill, and what is being spilled is the water.

So:

• effundat aquam = spill the water

That makes aquam accusative.

Because it follows the preposition e meaning out of or from.

The preposition ē / ex takes the ablative case, so:

• e catino = out of the bowl / from the bowl

That is why catinus becomes catinō here.

Both e and ex mean the same thing here: out of or from.

Latin often uses:

• ex before vowels
• e before consonants

Since catino begins with a consonant, e catino is perfectly normal.

You may still sometimes see ex before consonants too, but e catino is the expected form.

The sentence breaks down like this:

• Mater = subject
• infantem monet = warns the child
• ne aquam e catino effundat = not to spill the water from the bowl

So structurally it is:

• [Subject] [person warned] [verb of warning] [ne + subjunctive clause]

A very literal layout would be:

• Mother warns the child that he/she not spill the water from the bowl

Natural English turns that into:

• The mother warns the child not to spill the water from the bowl

Because Latin often places the verb at the end of its clause, especially in careful or neutral prose.

In the subordinate clause:

• ne aquam e catino effundat

the verb effundat comes last, which is very common Latin word order.

Latin word order is more flexible than English because the grammatical roles are shown by case endings, not mainly by position. So the sentence could be rearranged in other ways, but this order is very natural.

Not necessarily. Latin infans, infantis can mean a very young child, but it is often broader than English infant.

Depending on context, it may mean:

• infant
• baby
• small child

So infantem here is simply the child or the little child. English may or may not want the more specific word infant.

Not exactly in the usual beginner sense.

A learner might notice ne + subjunctive and think of a negative purpose clause, but here the clause is better understood as the content of the warning:

• She warns the child not to spill the water

So this is more like a subordinate clause after a verb of warning/command, not a clause meaning in order that ... not.

That distinction matters because the clause is not answering why she warns him, but what she warns him not to do.