Mindjárt felhívom a barátnőmet, csak előbb befejezem az e-mailt.

Mindjárt means something like in a moment, right away, or very soon.

In this sentence, it signals that the phone call will happen almost immediately, but not necessarily this exact second. It is often a little softer than azonnal, which is more like immediately.

So here mindjárt fits the idea of: I’m about to do it, just let me finish one thing first.

Hungarian very often uses the present tense to talk about the future when the time is already clear from context.

Here, words like mindjárt and előbb make the timing obvious, so Hungarian does not need a separate future form.

• felhívom = literally I call it/her, but here it means I’ll call
• befejezem = literally I finish it, but here it means I’ll finish

This is completely normal Hungarian. English usually prefers will, but Hungarian often does not.

Felhívom is a verb with a prefix:

• hív = to call, invite
• felhív = to call up, phone

In modern Hungarian, felhív is the normal verb for calling someone on the phone.

So felhívom breaks down roughly as:

• fel- = verbal prefix
• hív = call
• -om = I
  • definite object

So the whole form means I call him/her/it or, in context, I’ll call her.

This is about verb prefixes and word order.

In a neutral affirmative sentence, the prefix usually stays before the verb:

• Felhívom a barátnőmet. = I’ll call my girlfriend.

But the prefix can move after the verb in certain situations, especially with:

• focus
• negation
• questions
• sometimes an ongoing/process meaning

For example:

• Nem hívom fel a barátnőmet. = I’m not calling my girlfriend.
• A barátnőmet hívom fel. = It’s my girlfriend that I’m calling.
• Felhívod? / Hívod fel? = depending on structure and emphasis

So in your sentence, felhívom is the normal neutral order.

Hungarian normally uses the definite article before a possessed noun in ordinary speech:

• a barátnőm = my girlfriend / my female friend
• a barátnőmet = my girlfriend / my female friend, as the object

Even though English does not say the my girlfriend, Hungarian often does use the article in this kind of phrase.

So:

• a = the
• barátnőm = my girlfriend / my female friend
• barátnőmet = my girlfriend / my female friend in the accusative

Leaving out the article here would sound unusual or literary to most learners.

Barátnőmet contains:

• barátnő = girlfriend / female friend
• -m = my
• -t = accusative marker, showing it is the direct object

There is also an extra linking vowel in the full form, so:

• barátnőm = my girlfriend / my female friend
• barátnőmet = my girlfriend / my female friend, as the thing/person being called

This is why felhívom a barátnőmet means I’m calling my girlfriend / my female friend.

It can mean either one.

• barátnő can mean girlfriend
• it can also mean female friend

So a barátnőmet may mean:

• my girlfriend
• my female friend

The correct interpretation depends on context. Hungarian does not always force the distinction the way English often does.

Hungarian has two forms of the definite article:

• a before consonant sounds
• az before vowel sounds

Since e-mail begins with a vowel sound, Hungarian uses az:

• az e-mail

Then the object ending -t is added:

• az e-mailt

So this part means the e-mail as the direct object of befejezem.

Those endings are part of the definite conjugation.

Hungarian verbs change depending on whether the object is:

• indefinite / non-specific
• definite / specific

Here both objects are definite:

• a barátnőmet = my girlfriend / female friend, a specific person
• az e-mailt = the e-mail, a specific message

So Hungarian uses definite verb forms:

• felhívom
• befejezem

Compare:

• Felhívok valakit. = I’ll call someone.

• Felhívom a barátnőmet. = I’ll call my girlfriend.

• Befejezek egy e-mailt. = I’ll finish an e-mail.
• Befejezem az e-mailt. = I’ll finish the e-mail.

This is one of the big grammar features English speakers usually need to get used to.

Together, csak előbb means something like:

• just first
• only first
• more naturally in English: just let me first... or but first...

The two words contribute slightly different things:

• csak = only / just
• előbb = earlier / first / before that

In this sentence, csak softens the delay. It gives the feeling of:

I’ll do that in a second, I just need to finish the e-mail first.

So csak is not really about strict logical only here; it is more like conversational just.

Előbb often means earlier, sooner, or first/before that, depending on context.

Here it means before that or first:

• csak előbb befejezem az e-mailt = I’ll just finish the e-mail first

Hungarian often uses előbb very naturally in this kind of everyday sentence when one action happens before another.

So it does not have to mean a formal sequence like firstly; it is a natural conversational word.

Hungarian usually leaves out subject pronouns when they are already clear from the verb ending.

Both verbs show first person singular:

• felhívom = I call / I’ll call
• befejezem = I finish / I’ll finish

Because of that, én is not necessary.

If you added én, it would usually give extra emphasis:

• Én mindjárt felhívom a barátnőmet... = I’ll call my girlfriend soon... with stronger emphasis on I

Not completely. Hungarian word order is quite flexible, but it is not random. It depends a lot on topic, focus, and what is being emphasized.

The given sentence is a very natural neutral version:

• Mindjárt felhívom a barátnőmet, csak előbb befejezem az e-mailt.

This structure feels conversational and smooth:

• mindjárt sets the time
• felhívom gives the action
• a barátnőmet is the object
• then the second clause explains the delay

You could change the order for emphasis, but that would change the feel:

• A barátnőmet hívom fel mindjárt... = emphasis on my girlfriend
• Az e-mailt fejezem be előbb... = emphasis on the e-mail

So the original order is the most neutral everyday phrasing.