Ez a példa egyszerű, de a másik példa már nehezebb.

In Hungarian, when a demonstrative like ez (this) comes before a noun, the noun normally still keeps its article.

So:

• ez a példa = this example
• az a könyv = that book
• ez az alma = this apple

The article changes depending on the next word:

• a before a consonant
• az before a vowel

Since példa begins with p, you get ez a példa.

So for an English speaker, it helps to think of this as a normal Hungarian pattern: this + the + noun.

Hungarian often leaves out is in the present tense, third person singular, when the predicate is a noun or adjective.

So:

• Ez a példa egyszerű. = This example is simple.
• literally: This example simple.

This is completely normal in Hungarian.

But in other situations, a form of to be appears:

• Ez a példa egyszerű volt. = This example was simple.
• Én fáradt vagyok. = I am tired.
• Te kész vagy. = You are ready.

So the missing is here is not an omission in the casual sense; it is the standard grammar.

Adjectives do come before nouns when they directly describe the noun:

• egyszerű példa = a simple example

But in your sentence, egyszerű is not part of the noun phrase. It is the predicate:

• Ez a példa egyszerű. = This example is simple.

So the structure is:

• Ez a példa = the subject, this example
• egyszerű = what is being said about it, simple

That is why egyszerű comes after the noun here.

Compare:

• Ez egy egyszerű példa. = This is a simple example.
• Ez a példa egyszerű. = This example is simple.

Those are different sentence structures.

másik means the other one or another one, depending on context.

Here, a másik példa means the other example — a specific second example being contrasted with the first one.

Compare:

• a másik példa = the other example
• egy másik példa = another example

So the article matters:

• a másik points to a specific alternative
• egy másik introduces one among others

In this sentence, the speaker is clearly comparing two examples, so a másik példa is the natural choice.

Because the sentence is talking about a specific other example, not just any other example.

• a másik példa = the other example
• egy másik példa = another example

The definite article shows that both speaker and listener can identify which example is meant: the one contrasted with this example.

So the sentence sets up a pair:

• ez a példa = this example
• a másik példa = the other example

That makes the comparison very natural and specific.

már usually means already, but in real sentences it often adds a nuance rather than a strict literal meaning.

In this sentence:

• de a másik példa már nehezebb

it suggests something like:

• but the other example is already more difficult
• but the other example is now more difficult
• but the other example is noticeably more difficult

It marks a step or change: the first example is simple, but the second has moved into a harder category.

Sometimes English does not translate már very directly, but it still contributes an important feeling of progression or contrast.

nehezebb is the comparative form of nehéz.

• nehéz = difficult, hard
• nehezebb = more difficult, harder

Hungarian usually forms the comparative by adding -bb to the adjective. In some words, the stem changes a little as well, which is why nehéz becomes nehezebb, not just nehézbb.

So:

• egyszerű = simple
• nehéz = difficult
• nehezebb = more difficult

Unlike English, Hungarian does not need a separate word like more here; the comparative meaning is built into the adjective itself.

Hungarian word order is more flexible than English word order, and it often reflects emphasis and information structure rather than just grammar.

Here, the order is quite neutral:

• a másik példa = topic, what we are talking about
• már nehezebb = comment, what we say about it

So the sentence flows as:

• This example is simple, but as for the other example, it is already more difficult.

If you changed the word order, you could change the emphasis. For example:

• de már a másik példa nehezebb
• de a másik példa nehezebb már

These are possible in some contexts, but they sound different in focus or style. The version you have is a natural, standard way to say it.

Yes, often it could.

You can say:

• Ez a példa egyszerű, de a másik már nehezebb.

That would still be perfectly understandable: This example is simple, but the other one is already more difficult.

So why keep példa?

Because repeating it can make the contrast clearer and slightly more explicit, especially in teaching, explanation, or careful writing.

Both are natural:

• de a másik példa már nehezebb = a bit fuller, more explicit
• de a másik már nehezebb = shorter, more conversational