Vůbec neznám řešení.

Vůbec strengthens the negation. In this sentence, it means something like at all, in any way, or really not.

So:

• Neznám řešení. = I don’t know the solution.
• Vůbec neznám řešení. = I don’t know the solution at all. / I have no idea what the solution is.

It is a very common word with negatives in Czech.

The verb here is znát = to know, to be familiar with.

Neznám means I do not know / I am not familiar with.

Czech often distinguishes between:

• vědět = to know a fact, to know information
• znát = to know a person, place, thing, or be familiar with something

In this sentence, řešení is treated as something like the solution as an entity, so znát is natural.

Compare:

• Nevím odpověď. = less natural in standard Czech
• Neznám odpověď. = I don’t know the answer
• Nevím, jak to vyřešit. = I don’t know how to solve it

So neznám řešení is a normal Czech way to say I don’t know the solution.

Neznám is:

• 1st person singular
• present tense
• from the verb znát

So it means I do not know.

A few forms of znát in the present:

• znám = I know
• znáš = you know
• zná = he/she/it knows
• známe = we know
• znáte = you (plural/formal) know
• znají = they know

With negation:

• neznám = I do not know

Řešení is in the accusative singular, because it is the direct object of neznám.

The verb znát normally takes a direct object:

• Znám Petra. = I know Petr.
• Znám to místo. = I know that place.
• Neznám řešení. = I don’t know the solution.

A useful detail: řešení is a neuter noun of a type where the nominative and accusative singular look the same.

So here:

• nominative: řešení
• accusative: řešení

Even though the form does not change, its role in the sentence is accusative.

Řešení is a neuter noun meaning solution, solving, or resolution, depending on context.

It comes from the verb řešit = to solve.

This is a very common Czech pattern:

• řešit = to solve
• řešení = solution / solving

Other similar noun formations are:

• učit = to teach
• učení = learning / teaching / doctrine
• rozhodnout = to decide
• rozhodnutí = decision

So řešení is a verbal noun, built from a verb.

Czech has no articles, so there is no direct equivalent of a or the.

That means řešení can mean:

• a solution
• the solution
• sometimes just solution / solving

The exact meaning depends on context.

In Vůbec neznám řešení, English will often use the solution, but Czech does not need a separate word for that.

If Czech speakers want to be more specific, they can use other words, for example:

• to řešení = that solution / the solution
• nějaké řešení = some solution
• správné řešení = the correct solution

Yes. Czech word order is more flexible than English, although the basic version here is completely natural:

• Vůbec neznám řešení.

You may also hear:

• Řešení vůbec neznám.
• Řešení neznám vůbec.

These alternatives can shift the emphasis slightly.

Very roughly:

• Vůbec neznám řešení. = neutral, natural
• Řešení vůbec neznám. = emphasizes the solution
• Řešení neznám vůbec. = stronger emphasis at the end

For a learner, the original order is a very good default.

A rough pronunciation guide:

• Vůbec ≈ VOO-bets
• neznám ≈ NEZ-naam
• řešení ≈ the ř is difficult, something like a mix of r and zh; the whole word is roughly rzheh-shee-nee

A few key pronunciation points:

• ů is pronounced like a long ú sound: oo
• c is pronounced ts
• á is a long vowel
• š = sh
• í = long ee
• ř is a special Czech sound with no exact English equivalent

Stress in Czech usually falls on the first syllable of each word:

• VŮ-bec
• NE-znám
• ŘE-še-ní

Very often, yes, especially in everyday Czech. It commonly appears with negation to mean at all:

• Vůbec nerozumím. = I don’t understand at all.
• Vůbec to nevím. = I don’t know that at all.
• Vůbec neznám řešení. = I don’t know the solution at all.

But vůbec can also appear in other uses, for example to mean something like actually, in general, or as part of expressions like:

• Jak to vůbec víš? = How do you even know that?
• Co to vůbec je? = What even is that?

So it is strongly associated with negatives, but not limited to them.

A native speaker is much more likely to say:

• Neznám řešení.
• Nevím, jaké je řešení.
• Nevím, jak to vyřešit.

Nevím řešení sounds unnatural in standard Czech, because vědět usually introduces information or a clause rather than directly taking this kind of object in the same way.

So for a learner, it is safest to remember:

• znát + noun
• vědět + clause / information

Examples:

• Neznám odpověď. = I don’t know the answer.
• Nevím, co je správně. = I don’t know what is correct.

It is neutral and can be used in both spoken and written Czech.

Nothing in Vůbec neznám řešení is especially formal, literary, slangy, or rude. It is just a normal standard Czech sentence.

If you wanted a slightly more conversational alternative, you might also hear:

• Vůbec nevím, jak na to. = I really don’t know how to do it.
• Nemám tušení, jaké je řešení. = I have no idea what the solution is.

But the original sentence is perfectly standard and natural.