Mater filiam in peristylium ducit, ut lilia et violas spectet.

Because filiam is the direct object of ducit.

• mater = the mother, the subject
• ducit = leads
• filiam = the daughter, the person being led

In Latin, a direct object is often put in the accusative case, and filiam is the accusative singular of filia.

Because here in shows motion into a place.

Latin often uses:

• in + accusative = into / movement toward a place
• in + ablative = in / inside / location without movement

So:

• in peristylium = into the peristyle
• if it were talking about being inside it already, Latin might use in peristyliō

A peristylium is a peristyle, a colonnaded courtyard or open central area in a Roman house, usually surrounded by columns.

A learner may notice that this is not a very familiar English word, because it refers to a specifically Roman architectural feature.

Because it is inside an ut-clause of purpose.

After ut meaning so that or in order that, Latin normally uses the subjunctive mood. So:

• spectat = she looks at / she is looking at (indicative)
• spectet = that she may look at / so that she might look at (subjunctive)

In this sentence, ut ... spectet explains the purpose of the mother’s action.

The subject of spectet is understood from the context as filiam.

So the idea is:

• The mother leads her daughter into the peristyle
• so that the daughter may look at the lilies and violets

Latin often leaves out subject pronouns when they are understood. Here, the daughter is the natural understood subject of the purpose clause.

Because Latin very often does not need subject pronouns.

The verb ending itself gives information about the person and number:

• spectet = he/she/it may look at

Then the context tells you which person is meant. In this sentence, context strongly suggests the daughter.

They are the direct objects of spectet, so they are in the accusative case.

• lilia is the accusative plural of lilium (lily), a neuter noun
• violas is the accusative plural of viola (violet), a feminine noun

The forms are different because the nouns belong to different genders and declension patterns, but both are functioning as objects of spectet.

Because neuter nouns in Latin have a special pattern:

• the nominative plural
• and the accusative plural

are usually the same.

So for lilium:

• nominative plural = lilia
• accusative plural = lilia

That is normal for neuter nouns.

This is ut introducing a purpose clause.

In this sentence, ut means something like:

• so that
• in order that

A very common pattern in Latin is:

• main verb + ut
  • subjunctive

Here:

• ducit = she leads
• ut ... spectet = so that ... may look

So the clause answers the question why?

Yes. Ducit is present tense, third person singular, from ducere.

Depending on context, Latin present tense can be translated as:

• leads
• is leading
• sometimes even more flexibly depending on the passage

So mater filiam ... ducit can mean either the mother leads her daughter... or the mother is leading her daughter...

Because Latin often expresses possession or relationship simply through context.

Mater filiam ducit literally says the mother leads the daughter, but in natural English we often say her daughter because that is what the context suggests.

Latin does not always need a possessive adjective like suam. If the writer wanted extra emphasis or clarity, they could say mater filiam suam ducit, but it is not necessary.

Mater is nominative singular, because it is the subject of the sentence.

Even though mater does not have the very common -a ending that many learners expect in the nominative singular, it is still nominative. It is a third-declension noun:

• nominative singular: mater
• accusative singular: matrem

So here mater is the one performing the action.

Yes. It is a perfectly natural Latin word order, though Latin word order is more flexible than English word order.

A few things to notice:

• mater comes first, which gives the subject prominence
• filiam comes before the destination phrase
• ducit comes before the purpose clause
• ut ... spectet comes at the end, which is very common for a purpose clause

Latin relies more on endings than on strict word order, so the sentence could be rearranged in other ways without changing the basic meaning, though the emphasis might shift.