Huic puellae duo asini sunt, et eos mane ad agrum ducit.

Because Latin often expresses possession with the dative of possession plus a form of esse (to be).

So:

• Huic puellae duo asini sunt
  literally = To this girl there are two donkeys
• natural English = This girl has two donkeys

Here, huic puellae is dative singular, not the subject. The actual grammatical subject is duo asini.

Latin can also say haec puella duos asinos habet = this girl has two donkeys, using habet, but the sentence you were given uses the very common possessive pattern with sunt.

Because puellae can represent more than one case/number form:

• genitive singular = of the girl
• dative singular = to/for the girl
• nominative plural = girls

You have to decide from the context. Here, huic tells you what is going on:

• huic = to this / for this in the dative singular
• so puellae must also be dative singular

That is why huic puellae means to this girl, not these girls.

Because duo asini is the subject of sunt.

In Huic puellae duo asini sunt:

• huic puellae = possessor, in the dative
• duo asini = the things possessed, and also the grammatical subject
• sunt = are

Since duo asini is the subject, it must be in the nominative plural.

If the donkeys were a direct object, you would expect accusative forms such as duos asinos.

Because duo has to agree with asini, which is masculine plural nominative.

The forms of two are:

• duo = masculine
• duae = feminine
• duo = neuter

Since asinus is a masculine noun, the correct form is duo asini.

Eos is a third-person plural masculine accusative pronoun, meaning them.

It refers back to duo asini:

• duo asini = two donkeys
• eos = them

In the second clause:

• et eos mane ad agrum ducit
  = and she leads them to the field in the morning

Because ducit takes a direct object, the pronoun must be in the accusative, so eos is exactly what we expect.

For the same basic reason English uses them instead of repeating the donkeys.

Latin often avoids unnecessary repetition when the reference is already clear. So:

• et eos ducit = and she leads them
• instead of repeating et asinos ducit

Repeating the noun would still be possible, but eos is smoother and more natural here.

Here mane is an adverb, meaning in the morning or simply morningtime.

So:

• mane ducit = she leads ... in the morning

It is not a noun in a case form here; it is functioning adverbially, telling when the action happens.

Because ad with the accusative usually indicates motion toward a place.

So:

• ad agrum = to the field

Here:

• ducit ad agrum = she leads them to the field

The noun ager, agri is masculine, and its accusative singular is agrum, which is why you see ad agrum.

Because the subject of ducit is not the donkeys. The understood subject is she, referring to the girl.

So in the second clause:

• (ea) ducit = she leads
• eos = them (the object)

That is why the verb is third person singular:

• ducit = she/he leads

If the donkeys were doing the action, you would need a plural verb.

Because Latin verb endings usually already show the person and number.

• ducit = he/she/it leads

So Latin often leaves the subject pronoun unspoken unless it is needed for emphasis or contrast.

In this sentence, the subject is understood from context to be the girl mentioned earlier.

The word order matters less in Latin than in English because the case endings show the relationships between words.

This sentence is arranged as:

• Huic puellae = first, setting up the possessor
• duo asini sunt = then the possessed things
• et eos mane ad agrum ducit = then what she does with them

Latin could rearrange parts of this without changing the core meaning, as long as the forms stay the same. But the given order is natural and clear.

Yes. That would also mean this girl has two donkeys.

The difference is mainly in construction:

• Huic puellae duo asini sunt
  literally to this girl there are two donkeys
• Haec puella duos asinos habet
  literally this girl has two donkeys

Both are good Latin. The first uses the dative of possession; the second uses the ordinary verb habet. A learner should be comfortable with both patterns.