Kérek egy másikat.

A simple breakdown is:

• kérek = I ask for / I’d like
• egy = a / one
• másikat = another one as the direct object

So the sentence is built as:

• verb: kérek
• object: egy másikat

Hungarian often marks the object with an ending, rather than depending as heavily on word order as English does.

Because Hungarian usually leaves out subject pronouns when they are not needed.

The verb form kérek already tells you the subject is I. So:

• Kérek egy másikat. = I’d like another one.

If you do add én, it gives emphasis or contrast:

• Én kérek egy másikat. = I’m the one who wants another one / I want another one

So the version without én is the normal neutral one.

This is a very common Hungarian question, because Hungarian has two kinds of verb conjugation here: indefinite and definite.

• kérek = indefinite conjugation
• kérem = definite conjugation

You use the indefinite form when the object is not specific/definite.
In egy másikat, the object is indefinite: another one, not the other one.

So:

• Kérek egy másikat. = I’d like another one.
• Kérem a másikat. = I’d like the other one.

That is why kérek is correct here.

másikat is the word másik with object marking.

• másik = the other / another
• másikat = another one as a direct object

In this sentence, másik is being used on its own, without a noun after it, so it means another one.

For example, if the hidden noun is shirt, then:

• Kérek egy másikat. = I’d like another one.

Hungarian does not need to repeat the noun if the context already makes it clear.

Because -t is the usual accusative ending in Hungarian. The accusative marks the direct object.

Here, the direct object is another one, so másik takes the accusative:

• másik → másikat

The extra vowel before -t is there for pronunciation and normal Hungarian word formation. So you do not get másikt, but másikat.

Because egy can mean either one or a/an, just like an indefinite article.

In this sentence it helps express another one / another item:

• egy másikat = another one

So egy is very natural here. It does not have to sound strongly numerical; often it simply works like a/an.

Yes. That is very common.

Hungarian often allows adjectives or adjective-like words to stand in for a noun when the noun is understood from context.

So if you are choosing between two cakes, two shirts, two tickets, two plates, etc., you can just say:

• Kérek egy másikat.

The missing noun is understood from the situation.

This is an important distinction.

• más = different / something else
• másik = the other one / another one

In many situations, másik is used when choosing an alternative item of the same type.

Compare:

• Kérek mást. = I’d like something else.
• Kérek egy másikat. = I’d like another one.

So in your sentence, másikat is the right choice because the idea is not just something different, but another one of the same kind.

Yes, it is normally acceptable and natural in everyday situations like shops, cafés, bakeries, markets, or restaurants.

It is direct, but not rude by itself.

Still, there are softer or more polite alternatives, for example:

• Szeretnék egy másikat. = I’d like another one.
• Szeretnék kérni egy másikat. = I would like to ask for another one.
• Kaphatok egy másikat? = Can I get another one?

So Kérek egy másikat is perfectly usable, but not the softest possible version.

Yes. Hungarian word order is flexible, and changes in order often change emphasis rather than basic meaning.

The neutral version is:

• Kérek egy másikat.

You can also say:

• Egy másikat kérek.

This puts more emphasis on another one.

So both are possible, but they may sound slightly different in focus.

A careful pronunciation is approximately:

• kérek = /ˈkeːrɛk/
• egy = /ɛɟ/
• másikat = /ˈmaːʃikɒt/

A few useful pronunciation notes:

• é is a long vowel
• s in Hungarian sounds like English sh
• gy is a soft consonant, somewhat like the dy sound in some pronunciations of duke
• stress is on the first syllable of each word: KÉ-rek egy MÁ-si-kat

Use a másikat when you mean the other one, a specific alternative already identifiable in the situation.

Compare:

• Kérek egy másikat. = I’d like another one.
• Kérem a másikat. = I’d like the other one.

Notice that the verb changes too:

• kérek with an indefinite object
• kérem with a definite object

So the sentence changes both in the article and in the verb form.