A lány lassan oldja meg a feladatot, de a megoldás helyes.

A / az is the Hungarian definite article, like English the.

Hungarian uses:

• a before a consonant sound
• az before a vowel sound

So here:

• a lány
• a feladatot
• a megoldás

all begin with consonant sounds, so a is correct.

Because feladatot is the direct object of the verb, and Hungarian marks direct objects with the accusative ending -t.

So:

• feladat = task, exercise, problem
• feladatot = the task / the exercise as the thing being solved

The -o- before -t is just a linking vowel that makes the word easier to pronounce.

Because Hungarian has a definite conjugation and an indefinite conjugation.

Here the object is definite: a feladatot = the task, so the verb also takes a definite form:

• oldja = he/she solves it

Compare:

• megold egy feladatot = solves a task
• megoldja a feladatot = solves the task

So oldja is used because the sentence has a definite direct object.

The full verb is megold = solve.

In Hungarian, meg is a verbal prefix, and these prefixes often move away from the verb in certain sentence patterns.

A very useful learner rule is:

• neutral form: megoldja
• if another element is strongly highlighted right before the verb, the prefix often moves after the verb: oldja meg

So in this sentence:

• lassan oldja meg

lassan is the highlighted element before the verb, so meg comes after oldja.

Meg- often gives a sense of completion, result, or successful finishing.

With this verb:

• old can mean things like loosen, untie, or in some contexts solve
• megold is the standard verb for solve

So meg- helps make the idea more result-oriented: not just working on something, but bringing it to a solution.

That is also why the noun megoldás means solution.

Lassan is an adverb meaning slowly.

It is related to the adjective:

• lassú = slow

So:

• lassú lány = a slow girl
• lassan oldja meg = she solves it slowly

Many Hungarian adverbs are formed from adjectives with endings like -an / -en, though the exact form is not always fully predictable.

In Hungarian, the present-tense verb to be is usually omitted in the third person singular and third person plural when the predicate is a noun or adjective.

So:

• a megoldás helyes = the solution is correct

There is no van here.

But Hungarian does use van in other situations, for example:

• A megoldás helyes volt. = The solution was correct.
• Én fáradt vagyok. = I am tired.

They refer to two different parts of the situation:

• feladat = the task, exercise, or problem to be solved
• megoldás = the solution or answer

So the sentence first talks about doing the task, then about the correctness of the result.

Also, megoldás is built from:

• megold = solve
• -ás = a noun-forming suffix

So megoldás literally means something like solving / solution.

No. Hungarian word order is flexible, and it often shows emphasis, topic, and focus, not just basic grammar roles.

In this sentence:

• A lány is the topic: we are talking about the girl
• lassan is prominent before the verb
• oldja meg a feladatot is the predicate

If you change the order, the emphasis changes. For example:

• A lány oldja meg a feladatot. = It is the girl who solves the task.
• A feladatot a lány oldja meg. = It is the task that the girl solves / As for the task, the girl solves it.

So Hungarian word order is not random, but it is much more meaning-sensitive than English word order.

It can mean either, depending on context.

Hungarian present tense often covers both:

• simple present: solves
• present progressive-like meaning: is solving

So this sentence could describe:

• a general way she works, or
• what she is doing right now

The surrounding context, and sometimes intonation, tell you which meaning is intended.

Because de means but, and in Hungarian it is normally separated by a comma when it connects two clauses.

So:

• ..., de ... = ..., but ...

This works very much like English punctuation in the same kind of sentence.