In curru duo dolia et unum canistrum vehuntur.

Because in can take two different cases:

• ablative for location: in the cart / in the wagon
• accusative for motion into: into the cart / into the wagon

Here the sentence tells you where the barrels and basket are being transported, not that they are moving into the cart. So Latin uses in curru.

Curru is ablative singular.

The noun is currus, a fourth-declension masculine noun. After in with the meaning in/on, the ablative is expected.

So:

• currus = the cart/chariot/wagon
• in curru = in the cart / on the wagon

They are in the nominative, because they are the subject of the verb vehuntur.

Even though English might naturally think of these things as the objects of carrying, in Latin this sentence is passive:

• vehuntur = are carried / are transported

So the things being carried become the grammatical subject:

• duo dolia et unum canistrum = two barrels and one basket

Because dolium is a second-declension neuter noun, and neuter nouns of this declension normally form the nominative and accusative plural in -a.

So:

• singular: dolium
• plural: dolia

This is a very important Latin pattern:

• neuter singular often ends in -um
• neuter plural often ends in -a

Because Latin numbers can agree with the nouns they modify in gender, number, and case.

Dolia is:

• neuter
• plural
• nominative

So two must also appear in the matching form:

• duo

This is the correct nominative neuter plural form of two.

Because canistrum is neuter singular, and the numeral/adjective one must agree with it.

The forms are:

• masculine: unus
• feminine: una
• neuter: unum

Since canistrum is neuter, Latin uses unum canistrum.

Because the whole subject is compound:

• duo dolia
• et
• unum canistrum

Together, that means more than one thing, so the verb is plural.

In English we do the same:

• Two barrels and one basket are being carried not
• Two barrels and one basket is being carried

So Latin uses vehuntur, the third person plural form.

Vehuntur is:

• present tense
• indicative mood
• passive voice
• third person plural

It comes from the verb veho, vehere, meaning to carry, to transport, or to convey.

So vehuntur means:

• they are carried
• they are being transported

Here they refers to duo dolia et unum canistrum.

Because the sentence is focused on the things being transported, not on who is transporting them.

Latin often uses the passive when the doer is unknown, unimportant, or simply not the point.

So this sentence means something like:

• Two barrels and one basket are being transported in the wagon.

If Latin wanted an active sentence, it would need someone doing the carrying, for example:

• servi duo dolia et unum canistrum vehunt
  The slaves carry two barrels and one basket.

Not in the same way it is in English. Latin word order is much freer because the endings show each word’s role.

So these are all broadly possible with different emphasis:

• In curru duo dolia et unum canistrum vehuntur.
• Duo dolia et unum canistrum in curru vehuntur.
• Vehuntur in curru duo dolia et unum canistrum.

The version given starts with In curru, which draws attention first to the location.

It can depend on how you would express it naturally in English.

Latin in with vehicles often covers what English may say as either:

• in the cart
• on the wagon
• sometimes even in the chariot

Latin is not always making the same inside/on-top-of distinction that English makes. The important idea is that the objects are being transported by means of / within that vehicle.

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

So:

• curru can mean in a wagon or in the wagon
• unum canistrum can mean one basket
• duo dolia can mean two barrels

Whether something is definite or indefinite usually has to be understood from the context.

Et simply means and. It joins the two parts of the subject:

• duo dolia
• unum canistrum

So:

• duo dolia et unum canistrum = two barrels and one basket

It is the most straightforward way to connect them.