Annak ellenére, hogy nehéz, fontos a szelektív hulladékgyűjtés.

It means although, even though, or more literally despite the fact that.

In this sentence:

• Annak ellenére, hogy nehéz, fontos a szelektív hulladékgyűjtés.

the part annak ellenére, hogy nehéz introduces a contrast:

• Even though it is difficult...
• Although it is difficult...

This is a very common Hungarian pattern.

Because ellenére is a postposition that normally goes with a noun or pronoun.

So Hungarian says something like:

• valami ellenére = despite something
• annak ellenére = despite that

Then hogy introduces the clause that explains what that refers to:

• annak ellenére, hogy nehéz = despite the fact that it is difficult

So the structure is:

• annak = of that / that
• ellenére = despite / in spite of
• hogy = that

As a unit, it functions like although.

Annak is the dative form of az (that).

• az = that
• annak = to that / of that, depending on the structure

With ellenére, Hungarian uses this form:

• valaminek az ellenére / valami ellenére = despite something

So annak ellenére is the standard grammatical form. You should learn it as a fixed expression.

Hogy introduces a subordinate clause, often like English that.

Here:

• annak ellenére, hogy nehéz

literally means:

• despite that, that it is difficult

That sounds awkward in English, but it is normal in Hungarian.

So hogy nehéz is the clause attached to annak ellenére.

In Hungarian, you often do not need an explicit subject when English uses it in impersonal expressions.

So:

• nehéz = it is difficult / difficult

There is no separate Hungarian word for the dummy subject it here.

Compare:

• Nehéz. = It is difficult.
• Fontos. = It is important.

So in hogy nehéz, the meaning is simply that it is difficult.

Both are possible, but the word order changes the focus slightly.

• A szelektív hulladékgyűjtés fontos.
  = Selective waste collection is important.
  This is a more neutral, straightforward statement.

• Fontos a szelektív hulladékgyűjtés.
  = Selective waste collection is important.
  This gives a bit more prominence to fontos.

After the introductory clause annak ellenére, hogy nehéz, starting the main clause with fontos sounds very natural.

Hungarian word order is influenced a lot by information structure and focus, not just grammar.

Because a szelektív hulladékgyűjtés is a definite noun phrase:

• a = the
• szelektív hulladékgyűjtés = selective waste collection

Hungarian often uses the definite article where English may or may not use the depending on style.

Here a szelektív hulladékgyűjtés refers to the general concept/activity, and using a is natural.

Because Hungarian compound spelling has rules about when parts are written together and when they remain separate.

Here:

• hulladékgyűjtés = waste collection
  This is a compound.
• szelektív hulladékgyűjtés = selective waste collection
  Here szelektív is an adjective modifying the compound noun.

So the whole phrase is not written as one giant word. The adjective stays separate from the noun phrase it modifies.

It is a compound noun:

• hulladék = waste
• gyűjtés = collecting / collection

So:

• hulladékgyűjtés = waste collection

And then:

• szelektív hulladékgyűjtés = selective waste collection

This is a very common feature of Hungarian: new nouns are often formed by combining existing words.

Yes. A very natural alternative is:

• Bár nehéz, fontos a szelektív hulladékgyűjtés.

Here bár means although.

The difference is mainly stylistic:

• bár is shorter and simpler
• annak ellenére, hogy is a bit more explicit and slightly heavier in style, closer to despite the fact that

Both are correct.

Because the sentence contains a subordinate clause at the beginning.

Structure:

• Annak ellenére, hogy nehéz, = subordinate concessive clause
• fontos a szelektív hulladékgyűjtés. = main clause

Hungarian normally separates such clauses with commas.

So the commas help show where the introductory clause ends and the main statement begins.

Yes. Nehéz can mean:

• difficult
• hard
• sometimes even heavy, depending on context

In this sentence, the intended meaning is clearly difficult, not heavy.

So:

• hogy nehéz = that it is difficult

It sounds neutral to slightly formal.

Why?

• szelektív hulladékgyűjtés is a fairly formal or official-sounding term
• annak ellenére, hogy is a more elaborate connector than bár

So this sentence would fit well in:

• educational material
• public information
• environmental discussions
• semi-formal writing

In casual speech, someone might more often say:

• Bár nehéz, fontos szelektíven gyűjteni a hulladékot.

That means roughly:

• Although it’s difficult, it’s important to collect waste selectively.