Megkeverem a kártyapaklit, miközben te számolsz.

The base verb kever means to mix, and with cards it commonly means to shuffle. The prefix meg- often gives the idea of a completed, whole action.

So:

• keverem = I am mixing/shuffling it
• megkeverem = I shuffle it / I’ll shuffle it completely

In this sentence, megkeverem suggests a single completed action rather than just an ongoing process.

Because this is the definite conjugation.

Hungarian verbs often have two sets of endings:

• indefinite conjugation: used when there is no definite object
• definite conjugation: used when the direct object is definite

Here the object is a kártyapaklit = the deck of cards, which is definite, so the verb takes the definite 1st person singular ending:

• keverek = I shuffle/mix something
• keverem = I shuffle/mix it / the deck

Because számol here does not have a definite direct object.

In this sentence, számolsz simply means you count. It is being used intransitively, so the normal indefinite ending is used:

• számolsz = you count
• számolod a lapokat = you count the cards

So the difference is that megkeverem has a definite object, but számolsz does not.

The -t marks the accusative case, which is used for the direct object.

The basic noun is:

• kártyapakli = deck of cards

As the object of the verb, it becomes:

• kártyapaklit = the deck of cards

So -t is the normal object marker here.

Because the sentence refers to a specific deck, not just any deck.

• a kártyapaklit = the deck of cards
• egy kártyapaklit = a deck of cards

Using a makes the object definite, and that is one reason the verb appears in the definite conjugation: megkeverem.

Miközben is a conjunction meaning while, as, or meanwhile.

It introduces a clause that describes something happening at the same time as the action in the main clause.

So in this sentence, one action happens during the other:

• Megkeverem a kártyapaklit
• miközben te számolsz

That means the shuffling happens while the other person is counting.

That is true: Hungarian usually omits subject pronouns because the verb ending already shows the person.

So számolsz already means you count.

The pronoun te is included here for emphasis or contrast. It highlights the division of roles:

• I shuffle the deck
• you count

Without emphasis, you could also say:

• Megkeverem a kártyapaklit, miközben számolsz.

That is still grammatical, just less contrastive.

Formally, it is present tense.

However, Hungarian often uses the present tense for actions that are about to happen or are understood from context as future. So this sentence can mean either:

• something happening now, or
• something the speaker is about to do

The prefix meg- also helps give the sense of a complete action, which can make the sentence feel very natural in a future-like context.

Yes. Hungarian word order is fairly flexible, and changing it often changes emphasis rather than basic meaning.

For example:

• Megkeverem a kártyapaklit, miközben te számolsz.
  Neutral and natural.

• Miközben te számolsz, megkeverem a kártyapaklit.
  Starts with the while-clause.

• A kártyapaklit megkeverem, miközben te számolsz.
  Gives extra emphasis to the deck.

So the original order is natural, but not the only possible one.

Yes, verb prefixes can move, but in a neutral affirmative sentence they normally stay attached to the verb.

So:

• megkeverem = normal neutral form

Prefixes often separate when there is:

• negation
  
  • Nem keverem meg a kártyapaklit.
• strong focus
• certain verbal constructions

In this sentence, there is no reason to separate the prefix, so megkeverem is exactly what you would expect.

Yes, kártyapakli is one word. It is a compound noun:

• kártya = card
• pakli = deck/pack

Together, kártyapakli means deck of cards.

If the context is clear, speakers often just say:

• a paklit

That would sound perfectly natural if everyone already knows you are talking about a deck of cards.

They are not the same.

• kártyapaklit = the deck as a single unit
• kártyákat = the cards, as individual cards

When you shuffle, Hungarian very naturally uses pakli for the whole deck. So megkeverem a kártyapaklit sounds more idiomatic than talking about the cards individually.