Mi agordis la modemon kaj la enkursigilon.

In Esperanto, ordinary nouns normally end in -o. So an international word like modem gets adapted as modemo.

In this sentence, it becomes modemon because:

• modemo = modem
• -n = the direct object ending

So:

• modemo = a modem / modem
• modemon = a modem / the modem as the object of the verb

Agordis is the past-tense form of agordi.

It breaks down like this:

• agord- = the verb root
• -is = past tense

So:

• agordi = to configure, set, adjust
• agordas = configure / am configuring
• agordis = configured
• agordos = will configure

In this sentence, agordis means configured or set up.

Usually, no. Esperanto verbs do not change for person, so agordis by itself only tells you that the action is in the past. It does not tell you whether the subject is I, you, he, she, we, or they.

So Esperanto normally keeps the subject pronoun:

• Mi agordis = I configured
• Li agordis = He configured
• Ili agordis = They configured

Because of that, mi is normally necessary unless the subject is already very obvious from context.

Because they are the direct objects of the verb agordis.

In Esperanto, the direct object usually takes the ending -n. English marks this mostly by word order, but Esperanto often marks it directly on the noun.

Here:

• Mi = the subject, the person doing the action
• agordis = configured
• la modemon kaj la enkursigilon = the things being configured

So both the modem and the router are direct objects, which is why both nouns take -n.

Each direct-object noun normally gets its own accusative ending.

So Esperanto says:

• la modemon kaj la enkursigilon

not:

• la modemo kaj la enkursigilon

Both items are objects of agordis, so both are marked.

This is very normal in Esperanto. If there were adjectives, they would also match:

• la novan modemon kaj la malnovan enkursigilon

Because both nouns are definite: the modem and the router.

In Esperanto, la works like English the, and it is usually placed before each noun when both are definite:

• la modemon kaj la enkursigilon

If you said:

• la modemon kaj enkursigilon

that would usually sound more like:

• the modem and a router

So repeating la makes it clear that both devices are specific, known ones.

Enkursigilo is the normal Esperanto word for router.

It is built from several parts:

• en-
• kurs
• -ig-
• -il-
• -o

A learner does not need to analyze every part perfectly every time, but the general idea is a device used to route/direct traffic.

The important practical point is:

• enkursigilo = router
• enkursigilon = router as a direct object

Esperanto often builds technical vocabulary this way: one long word made from smaller meaningful pieces.

Yes, you could move them, because the -n ending shows that they are the objects.

The normal, neutral order is:

• Mi agordis la modemon kaj la enkursigilon.

But Esperanto can also say:

• La modemon kaj la enkursigilon mi agordis.

That is still understandable because modemon and enkursigilon both have -n, so their role in the sentence is clear.

Still, for beginners, the standard subject–verb–object order is the safest choice.

A helpful pronunciation guide is:

Mi a-GOR-dis la mo-DE-mon kaj la en-kur-si-GI-lon.

A few key points:

• Every letter is pronounced.
• Stress in Esperanto is usually on the second-to-last syllable of each word.
• kaj sounds roughly like kai.

Word by word:

• Mi = mee
• agordis = a-GOR-dis
• la = lah
• modemon = mo-DE-mon
• kaj = kai
• enkursigilon = en-kur-si-GI-lon

No. La always stays la.

That is different from the nouns:

• la modemo = the modem
• la modemoj = the modems
• la modemon = the modem as object
• la modemojn = the modems as objects

The article does not change, but the noun does.

So in your sentence, la stays the same, while modemo and enkursigilo change to modemon and enkursigilon because they are direct objects.