A szellemi munka nehéz.

In Hungarian, the verb van (to be) is usually left out in the present tense, third person when one thing is being identified or described.

So:

• A szellemi munka nehéz. = Mental work is difficult.
• literally: The mental work difficult.

This omission is completely normal in Hungarian.

But the verb appears in other persons:

• A szellemi munka nehéz. = Mental work is difficult.
• A szellemi munka nehéz volt. = Mental work was difficult.
• A szellemi munka nehéz lesz. = Mental work will be difficult.
• A szellemi munka nehéz nekem. = Mental work is difficult for me.

And with I/you/we, you do use forms of van:

• Nehéz vagyok would mean I am heavy, not I am difficult
• A munka nehéz. = The work is difficult

So in this sentence, the missing is is just standard Hungarian grammar.

A is the definite article, so it means the.

• a munka = the work
• a szellemi munka = the mental/intellectual work

Hungarian has two forms of the definite article:

• a before most consonants
• az before vowels

For example:

• a munka = the work
• az iskola = the school

In many general statements, Hungarian often uses the definite article where English may use zero article or a more general expression. So A szellemi munka nehéz can still be understood as a general statement like Mental work is difficult.

Szellem is the noun. Depending on context, it can mean things like spirit, mind, or intellect.

To make it into an adjective meaning mental, intellectual, or of the mind, Hungarian adds the adjectival ending -i:

• szellem = spirit / intellect / mind
• szellemi = mental / intellectual

So:

• szellemi munka = mental work, intellectual work

This -i ending is very common in Hungarian for making adjectives from nouns:

• iskola = school → iskolai = school-related
• nemzet = nation → nemzeti = national
• történelem = history → történelmi = historical

So szellemi is simply the adjective form.

In this sentence, szellemi most naturally means mental or intellectual.

So szellemi munka usually means:

• mental work
• intellectual work
• work that uses the mind rather than physical labor

It does not usually mean spiritual work here.

That is important, because English speakers may connect spirit with religion or spirituality. Hungarian szellemi can sometimes relate to the mind/intellect rather than spirituality.

Compare:

• szellemi munka = mental / intellectual work
• fizikai munka = physical work

That contrast is very common in Hungarian.

Yes, Hungarian word order is flexible, but different orders give different emphasis.

The neutral order here is:

• A szellemi munka nehéz.

This is a plain statement: Mental work is difficult.

If you move things around, you may change the focus or emphasis. For example:

• Nehéz a szellemi munka.
  This can sound a little more like Mental work is difficult with focus on difficult.

In many basic sentences, the predicate adjective often comes at the end in neutral word order, so A szellemi munka nehéz is a very natural textbook-style sentence.

Hungarian adjectives do not agree with nouns in gender, and Hungarian has no grammatical gender like masculine/feminine/neuter.

So nehéz stays nehéz.

That means:

• nehéz munka = difficult work
• nehéz feladat = difficult task
• nehéz könyvek = difficult books

The adjective does not change for masculine/feminine, and usually not in the way learners from some European languages expect.

In this sentence, nehéz is a predicate adjective: it describes a szellemi munka. Hungarian keeps it simple here.

Yes. Nehéz can mean both heavy and difficult/hard, depending on context.

For example:

• A doboz nehéz. = The box is heavy.
• A feladat nehéz. = The task is difficult.
• A szellemi munka nehéz. = Mental work is difficult.

In your sentence, difficult is clearly the intended meaning, because mental work is not literally heavy.

This is very similar to how some English words also have more than one related meaning depending on context.

Yes. That would mean:

• Ez a szellemi munka nehéz. = This mental work is difficult.

The original sentence:

• A szellemi munka nehéz.

is more general. It can mean mental work is difficult or the mental work is difficult, depending on context.

If you want to point to a specific kind of work more clearly, adding ez a (this) can help.

So:

• A szellemi munka nehéz. = general or context-dependent
• Ez a szellemi munka nehéz. = this specific mental work is difficult

A simple pronunciation guide for an English speaker would be:

• A ≈ short open aw
• szellemi ≈ SEL-leh-mee
• munka ≈ MOON-kaw
• nehéz ≈ neh-HAYZ

A few useful points:

• Hungarian stress is usually on the first syllable of each word.
• sz is pronounced like English s in see
• plain s in Hungarian is pronounced like English sh
• é is a long vowel, roughly like ay in say, but cleaner and tenser

So nehéz has a long é, which matters.

A rough full reading:

aw SEL-leh-mee MOON-kaw neh-HAYZ

Yes, it is a very common and natural expression.

It usually refers to:

• mental work
• intellectual work
• non-physical work
• work involving thinking, planning, analysis, study, writing, etc.

A very common contrast is:

• szellemi munka = mental / intellectual work
• fizikai munka = physical work

So this sentence is useful not just grammatically, but also as a common real-life phrase.