Via dextra ad forum ducit, sed via sinistra ad portam.

Here via is the subject of the verb ducit, so it is in the nominative singular.

• via = the road / path
• ducit = leads

If it were a direct object, you would expect viam instead. In this sentence, the road is the thing doing the leading.

Because they are adjectives agreeing with via.

Latin adjectives must match the noun they describe in:

• gender
• number
• case

Since via is feminine singular nominative, the adjectives must also be feminine singular nominative:

• via dextra = the right-hand road
• via sinistra = the left-hand road

Their dictionary forms are:

• dexter, dextra, dextrum
• sinister, sinistra, sinistrum

Here they are adjectives describing via.

So:

• via dextra = right road
• via sinistra = left road

However, in other contexts dextra can mean right hand, and sinistra can mean left hand or left side. Latin words often have more than one use, but in this sentence they clearly describe via.

ducit is:

• 3rd person singular
• present tense
• indicative mood
• active voice

It comes from ducere, meaning to lead.

It is singular because the subject is singular: via.

So literally, via ... ducit means the road leads.

This is a very common feature of Latin: the verb can be left out when it is easily understood.

So:

• Via dextra ad forum ducit, sed via sinistra ad portam means
• Via dextra ad forum ducit, sed via sinistra ad portam ducit

English does this too sometimes, especially in comparisons:

• The right road leads to the forum, but the left one to the gate.

Latin often omits repeated words to avoid unnecessary repetition.

Because ad takes the accusative case when it means to or toward.

So:

• ad forum = to the forum
• ad portam = to the gate

The different endings come from the nouns themselves:

• forum is a neuter second-declension noun, and its accusative singular is also forum
• porta is a feminine first-declension noun, and its accusative singular is portam

So the case is the same in both phrases, even though the forms look different.

Because Latin word order is much more flexible than English word order.

Both noun-adjective orders are possible in Latin, but noun + adjective is very common:

• via dextra
• via sinistra

So this is a normal Latin way to say the right road and the left road.

English usually prefers adjective + noun, but Latin does not have to.

No. Latin word order is flexible because endings show the grammatical relationships.

This sentence is:

• Via dextra ad forum ducit, sed via sinistra ad portam.

But Latin could rearrange parts of it without changing the basic meaning, for example:

• Via dextra ducit ad forum
• Ad forum via dextra ducit

The chosen order here is natural and clear. It also creates a nice balance:

• via dextra ...
• sed via sinistra ...

That contrast is probably one reason for the arrangement.

Latin does not have definite or indefinite articles like English the or a/an.

So:

• via can mean a road or the road
• forum can mean a forum or the forum
• porta can mean a gate or the gate

You decide from context which English article to use when translating.

It is repeated for clarity and balance.

Compare:

• Via dextra ad forum ducit, sed via sinistra ad portam

This clearly sets up a contrast between:

• the right road
• the left road

Latin could sometimes omit the repeated noun if the meaning were obvious, but repeating via makes the sentence neat and symmetrical.

sed means but.

It joins the two clauses and shows a contrast:

• the right road goes one way
• but the left road goes another way

So sed is just a straightforward coordinating conjunction introducing the contrast.