Puella septem flores et decem folia in horto numerat, dum soror eius cantat.

Puella is in the nominative singular, which is the case typically used for the subject of a finite verb in Latin. It means girl.

You can also tell it is the subject because it matches the verb numerat (counts), which is third person singular: the girl counts.

They are both direct objects of numerat, but they come from different kinds of nouns.

• flos, floris = flower
  
  • accusative plural: flores
• folium, folii = leaf
  
  • accusative plural: folia

So both words are in the accusative plural, but their endings differ because they belong to different declensions and genders.

Because folium is a neuter noun.

A very important Latin rule is:

• neuter nominative plural = neuter accusative plural
• and that ending is often -a

So:

• singular: folium
• plural nominative/accusative: folia

That is why folia is correct as the plural direct object.

No. Septem (seven) and decem (ten) are indeclinable cardinal numbers, so they do not change form for case, gender, or number.

They simply stay:

• septem
• decem

They modify flores and folia, but their own form does not change.

Because in can take two different cases depending on the meaning:

• in + ablative = in / on a place, with no motion
• in + accusative = into / onto a place, with motion toward it

Here the girl is counting in the garden, not moving into the garden, so Latin uses the ablative:

• hortus = garden
• horto = in the garden

Dum here means while.

It introduces a clause describing something happening at the same time as the main action:

• Puella ... numerat = the girl counts
• dum soror eius cantat = while her sister sings

Latin very often uses the present indicative after dum when describing an action going on at the same time as another action. So numerat and cantat are both present because the two actions are simultaneous.

This is a very common and important question.

• eius means his / her / its
• suus, sua, suum is a reflexive possessive, meaning his/her own, referring back to the subject of its own clause

In the clause dum soror eius cantat, the subject of that clause is soror. If you said soror sua, it would normally mean her own sister with reference to the sister herself, which does not make sense here.

But eius refers back to puella, the girl in the main clause:

• dum soror eius cantat = while her sister sings

So eius is the correct choice.

Latin has no articles like English the or a/an.

So:

• puella can mean girl, a girl, or the girl
• horto can mean in a garden or in the garden

The exact sense usually comes from context.

Yes. Latin word order is much more flexible than English word order because endings show the grammatical roles.

This sentence could be rearranged in several ways and still mean basically the same thing, for example:

• Puella septem flores et decem folia in horto numerat, dum soror eius cantat.
• In horto puella septem flores et decem folia numerat, dum soror eius cantat.
• Dum soror eius cantat, puella septem flores et decem folia in horto numerat.

The usual effect of changing the order is not to change the core meaning, but to change emphasis or style.

Yes. Numerat can govern more than one object when they are joined by et.

Here the girl is counting:

• septem flores
• et decem folia

These are two coordinated accusative phrases, both depending on numerat.

So the structure is basically:

• The girl counts seven flowers and ten leaves.

Both are:

• present
• active
• indicative
• third person singular

So:

• numerat = he/she/it counts
• cantat = he/she/it sings

The subject tells you who is doing the action:

• puella numerat = the girl counts
• soror eius cantat = her sister sings

Soror is nominative singular. It is the subject of the subordinate clause introduced by dum.

So in:

• dum soror eius cantat

the subject is soror eius (her sister), and the verb is cantat (sings).

It is separate from the main clause subject puella, even though the two clauses belong to the same sentence.