Gyakorlati problémát oldunk meg.

A natural breakdown is:

• gyakorlati = practical
• problémát = problem in the accusative case, so it is the direct object
• oldunk = we solve / we are solving
• meg = a verbal prefix that helps make the verb mean solve completely / resolve

So the structure is basically:

[adjective + object] + [verb] + [prefix]

More literally, you can think of it as:

A practical problem, we solve.

But in normal English, of course: We solve a practical problem or We are solving a practical problem.

Because it is the direct object of the verb.

In Hungarian, direct objects usually take the accusative ending -t. So:

• probléma = problem
• problémát = a problem / the problem as the thing being solved

The long vowel in -át happens because of how this noun takes the accusative form. So this is not just probléma + t mechanically in spelling; the form becomes problémát.

Because Hungarian adjectives usually do not agree with the noun the way they do in many Indo-European languages.

So:

• gyakorlati probléma = practical problem
• gyakorlati problémát = practical problem (as object)

Only the noun gets the accusative ending here, not the adjective.

That is very normal in Hungarian:

• jó könyv = good book
• jó könyvet = good book (object)

Not jót könyvet in this kind of structure.

Oldunk comes from the verb old, which means to solve, to undo, or to loosen, depending on context. In this sentence, it means solve.

The ending -unk tells you the subject is:

• first person plural = we

So:

• oldok = I solve
• oldasz = you solve
• old = he/she solves
• oldunk = we solve

In this sentence, oldunk is in the present tense.

Because meg changes the meaning of the verb.

Without meg, old can be broader, and depending on context it may sound less like successfully solving a problem to completion.

With meg, megold is the normal verb for solve / resolve a problem.

So:

• old = solve, loosen, undo, untie, etc. depending on context
• megold = solve, resolve

That is why this sentence uses meg.

Hungarian verbal prefixes often separate from the verb depending on sentence structure.

When the sentence is neutral and nothing special is being emphasized, you often get the prefix attached:

• Megoldunk egy gyakorlati problémát.

But if another part of the sentence is in focus, the prefix often moves after the verb:

• Gyakorlati problémát oldunk meg.

Here, gyakorlati problémát is in the focus position before the verb, so the prefix meg comes after oldunk.

This is a very common Hungarian pattern.

This is about the indefinite vs. definite conjugation in Hungarian.

Hungarian verbs can have two kinds of endings:

• indefinite conjugation
• definite conjugation

Here, the object is problémát with no definite article like a/az, and it is understood as a practical problem rather than the practical problem. Because the object is indefinite, the verb uses the indefinite form:

• oldunk meg = we solve
• oldjuk meg = we solve it / we solve the specific one

Compare:

• Gyakorlati problémát oldunk meg. = We solve a practical problem.
• A gyakorlati problémát oldjuk meg. = We are solving the practical problem.

So oldunk is the correct choice here.

Hungarian often leaves out the article where English would use a/an in a general statement, especially in certain styles or sentence patterns.

So both of these are possible:

• Egy gyakorlati problémát oldunk meg.
• Gyakorlati problémát oldunk meg.

The version without egy can sound a bit more general, concise, or focused on the type of thing being solved: a practical problem rather than, for example, a theoretical one.

So the lack of an article here is normal.

It can mean either, depending on context.

Hungarian present tense often covers both:

• simple present
• present continuous

So oldunk meg can be:

• we solve
• we are solving

The surrounding context tells you which is more natural in English.

Yes, Hungarian word order is much more flexible than English word order, but the different orders can change focus and emphasis.

For example:

• Megoldunk egy gyakorlati problémát.
  Neutral: We solve a practical problem.

• Gyakorlati problémát oldunk meg.
  Focus on practical problem: it is a practical problem that we are solving.

So the sentence you were given is not random word order; it suggests a particular information structure.

Then you would normally use:

• A gyakorlati problémát oldjuk meg.

Key changes:

• a = the
• problémát stays accusative because it is still the object
• oldjuk instead of oldunk because with a definite object, Hungarian usually uses the definite conjugation

So:

• Gyakorlati problémát oldunk meg. = We solve a practical problem.
• A gyakorlati problémát oldjuk meg. = We are solving the practical problem.