Эта головоломка очень трудная.

Because головоломка is a feminine singular noun.

In Russian, the word for this changes to match the noun’s gender, number, and case:

• этот = this (masculine)
• эта = this (feminine)
• это = this (neuter)
• эти = these (plural)

Since головоломка is feminine, you say эта головоломка.

A very common clue is the ending -а or -я in the dictionary form of a noun. Nouns with these endings are often feminine.

So:

• головоломка ends in -а
• therefore it is usually treated as feminine

That is why both эта and трудная also appear in feminine form.

Russian adjectives must agree with the noun they describe.

Since головоломка is:

• feminine
• singular
• nominative

the adjective must also be:

• feminine
• singular
• nominative

So:

• masculine: трудный
• feminine: трудная
• neuter: трудное
• plural: трудные

That is why the sentence says трудная.

It is in the nominative case.

This sentence is basically saying:

• This puzzle = subject
• is very difficult = description of the subject

In Russian, the subject of a sentence is normally in the nominative case. So:

• эта = nominative feminine singular
• головоломка = nominative singular
• трудная = nominative feminine singular

Everything matches.

In the present tense, Russian usually omits the verb to be.

So English:

• This puzzle is very difficult.

Russian:

• Эта головоломка очень трудная.

There is no present-tense is in normal Russian sentences like this.

If you are learning literally, the structure is closer to:

• This puzzle very difficult.

But in natural English, of course, you translate it with is.

Очень means very.

It usually goes before the adjective or adverb it modifies:

• очень трудная = very difficult

So the word order here is straightforward:

• Эта головоломка = this puzzle
• очень трудная = very difficult

Yes. That would simply mean:

• This puzzle is difficult.

Adding очень strengthens it:

• трудная = difficult
• очень трудная = very difficult

So очень is optional if you do not need the extra emphasis.

They are similar, but not always identical.

• трудный / трудная often means difficult, hard
• сложный / сложная often means complex, though it can also mean difficult

For a puzzle, both can be possible depending on what you want to emphasize:

• трудная = hard to solve
• сложная = complicated / intricate

In many everyday contexts, learners will hear both translated as difficult.

The ending -ая is a common feminine singular adjective ending in the nominative case.

So:

• трудный = masculine
• трудная = feminine

In careful pronunciation, -ая is roughly like -aya.

So трудная sounds approximately like TROOD-na-ya, with the stress on the first syllable.

The usual stress is:

• Э́та
• головоло́мка
• о́чень
• тру́дная

A rough guide:

• Э́та = EH-ta
• головоло́мка = ga-la-va-LOM-ka
• о́чень = O-chen’
• тру́дная = TROOD-na-ya

Stress matters in Russian, so it is good to learn words together with their stressed syllables.

Yes, Russian word order is more flexible than English, but the neutral, standard order here is:

• Эта головоломка очень трудная.

You may hear different orders for emphasis, for example:

• Эта головоломка трудная.
• Головоломка очень трудная.
• Очень трудная эта головоломка. — more emphatic or stylistically marked

For a learner, the original version is the safest and most natural starting point.

Not in the same way.

Это can mean this or it is / this is, but it does not replace эта before a feminine noun in this sentence.

Correct:

• Эта головоломка очень трудная. = This puzzle is very difficult.

You can also say:

• Это очень трудная головоломка. = This is a very difficult puzzle.

Notice the structure changes:

• это acts more like this is
• трудная still agrees with головоломка

So эта is the right determiner directly before головоломка in the original sentence.

The dictionary forms are:

• этот = this
• головоломка = puzzle
• очень = very
• трудный = difficult

In the sentence, some words change form:

• этот → эта to match a feminine noun
• трудный → трудная for the same reason

But головоломка and очень already appear in their normal dictionary forms here.