Mercator nobis duo pocula offert: unum carum, aliud vile.

Because nobis is the dative form of nos.

With offert (offers), the person receiving the thing is usually put in the dative:

• mercator nobis offert = the merchant offers to us
• nos would mean we/us in a different grammatical role, usually as a direct object, which is not what is needed here.

So:

• nobis = to us / for us
• nos = us as a direct object

Here pocula is the neuter plural accusative of poculum (cup).

A very common Latin pattern is:

• second-declension neuter singular: -um
• second-declension neuter plural: -a

So:

• poculum = cup
• pocula = cups

In this sentence, pocula is the direct object of offert, so it is accusative plural.

Because pocula is neuter, and the numeral two must agree with the noun.

The forms of two are irregular:

• masculine: duo
• feminine: duae
• neuter: duo

So with a neuter noun like pocula, Latin uses:

• duo pocula = two cups

Also, the plural accusative of a neuter noun is the same as the nominative plural, so pocula is correct here.

Because each word refers to one cup at a time.

The idea is:

• duo pocula = two cups
• then those two cups are described separately:
  • unum carum = one expensive
  • aliud vile = the other cheap

Latin is leaving out an understood noun:

• unum (poculum)
• aliud (poculum)

So the words are singular because each refers to a single cup, not both together.

They agree with the implied noun poculum, which is neuter.

Even though poculum is not repeated, it is still understood:

• unum (poculum)
• aliud (poculum)

Since poculum is neuter singular, the pronouns/adjectives referring to it must also be neuter singular:

• unum
• aliud

For the same reason: they describe the implied noun poculum.

So Latin understands:

• unum poculum carum
• aliud poculum vile

Both adjectives must agree with poculum in gender, number, and case:

• carum = neuter singular accusative
• vile = neuter singular accusative

They look different because they belong to different adjective patterns:

• carus, cara, carum = first/second-declension adjective
• vilis, vile = third-declension adjective

That is why one neuter form is carum and the other is vile.

Mercator is nominative singular, and it is the subject of offert.

The noun mercator means merchant and belongs to the third declension. Its nominative singular form is simply mercator.

In the sentence:

• Mercator ... offert the verb offert is he/she/it offers, so mercator is the one doing the action.

Offert is the third-person singular present active indicative of offerre.

So it means:

• he offers
• she offers
• it offers

Here it means the merchant offers.

Offerre is a compound of ob + ferre, and ferre is an irregular verb, so some of its forms do not look like a regular third-conjugation verb. But offert is the normal present form for he/she offers.

Latin word order is fairly flexible, because the endings show the grammatical roles.

So this sentence could be rearranged in various ways without changing the basic meaning, for example:

• Mercator nobis duo pocula offert
• Mercator duo pocula nobis offert
• Duo pocula mercator nobis offert

The chosen order can affect emphasis or style, but the endings still tell you:

• mercator = subject
• nobis = indirect object
• duo pocula = direct object

The part after the colon gives extra detail about the two cups:

• unum carum, aliud vile

Because Latin often omits a noun when it is obvious from the context.

Once the sentence has already said duo pocula, Latin does not need to repeat poculum twice. Instead, it uses:

• unum
• aliud

and the reader understands:

• one cup
• the other cup

English does this too:

• I saw two books: one long, the other short.

So this is a very natural kind of ellipsis in Latin.