Csatlakoztatom és újraindítom a modemet.

Because both verbs are in the 1st person singular definite present form.

In this sentence, the speaker is doing something to a specific object: a modemet = the modem. When Hungarian verbs take a definite direct object, they usually use the definite conjugation.

• csatlakoztatom = I connect it / I am connecting it
• újraindítom = I restart it / I am restarting it

That -om ending tells you:

• the subject is I
• the object is definite

Hungarian usually does not need subject pronouns when the verb ending already shows the subject.

So:

• csatlakoztatom already means I connect it
• újraindítom already means I restart it

You could add én for emphasis:

• Én csatlakoztatom és újraindítom a modemet.

But without emphasis, leaving out én is more natural.

Because modemet is the accusative form, used for the direct object.

The base noun is:

• modem

To make it the object, Hungarian adds the accusative ending -t. Because modem ends in a consonant, a linking vowel appears:

• modem → modemet

So:

• a modem = the modem
• a modemet = the modem, as the thing being acted on

A is the Hungarian definite article, meaning the.

So:

• a modemet = the modem

Its presence is also part of why the verbs use the definite conjugation. The modem is not just any modem; it is a specific one.

Here it means something like:

• I connect it
• I plug it in
• I attach it

The exact English wording depends on context. With a modem, plug in or connect is often the most natural translation.

This verb comes from csatlakoztat, which is a transitive verb, meaning it takes a direct object.

So in this sentence, the speaker is doing the connecting to the modem.

Because these are different verbs.

• csatlakozom comes from csatlakozik and usually means I join or I connect in an intransitive sense
• csatlakoztatom comes from csatlakoztat and means I connect something

So:

• csatlakozom a hálózathoz = I connect to the network
• csatlakoztatom a modemet = I connect the modem

In your sentence, the modem is the direct object, so the transitive verb csatlakoztat is needed.

It can be broken down like this:

• újra = again, re-
• indít = start
• -om = 1st person singular definite ending

So újraindítom literally means something like I start it again, which is why it is translated as I restart it.

Yes. The object a modemet is shared by both verbs.

So the sentence means:

• I connect the modem and restart the modem

Hungarian does not need to repeat the object if it is the same for both actions.

That is why:

• Csatlakoztatom és újraindítom a modemet.

is perfectly natural.

Because Hungarian allows the object to be understood with both verbs, and it is common not to repeat it.

The structure is essentially:

• [I connect] and [I restart] the modem

Hungarian can place the shared object after the coordinated verbs:

• Csatlakoztatom és újraindítom a modemet.

This is natural and efficient.

You could also say:

• A modemet csatlakoztatom és újraindítom.

But that changes the emphasis. Putting a modemet first highlights the modem.

Grammatically, it is present tense. However, in Hungarian, present forms can sometimes refer to the near future, depending on context.

So this sentence can mean:

• I am connecting and restarting the modem
• I’ll connect and restart the modem

The exact time reference usually comes from the situation, not just the verb form.

The sentence has a fairly neutral, natural word order.

• Csatlakoztatom és újraindítom a modemet.

This presents the two actions in a straightforward way.

If you move elements around, the emphasis changes. For example:

• A modemet csatlakoztatom és újraindítom.
  This puts more focus on the modem.

• Újraindítom a modemet.
  This focuses just on the restarting action.

So Hungarian word order is flexible, but changes in order often affect emphasis rather than basic meaning.