Mindkettő szép: az egyik porcelán dísztárgy, a másik utánzat.

Mindkettő means both or both of them.

It is made up of:

• mind = all / every
• kettő = two

So the idea is something like both of the two.

In this sentence, Mindkettő szép means Both are beautiful / Both are nice.

These are related, but they are used differently:

• mindkettő = both (ones)
  Used on its own, without a noun after it.
  Example: Mindkettő szép. = Both are beautiful.

• mindkét = both

  • a noun
    Example: Mindkét tárgy szép. = Both objects are beautiful.

• mindketten = both, usually for people as the subject
  Example: Mindketten itt vannak. = They are both here.

So in your sentence, mindkettő is used because the noun is not repeated.

Because mindkettő behaves grammatically more like a singular pronoun, even though its meaning is plural.

So Hungarian normally says:

• Mindkettő szép.

not:

• Mindkettő szépek.

This can feel strange to an English speaker, because English uses plural agreement with both. Hungarian does not always match English logic here.

In Hungarian, the verb to be is usually omitted in the present tense, third person, when the sentence means something like X is Y.

So:

• az egyik porcelán dísztárgy literally looks like the one porcelain ornament
• but it means one is a porcelain ornament

And:

• a másik utánzat = the other is an imitation

If the tense changed, the verb would appear:

• Az egyik porcelán dísztárgy volt. = One was a porcelain ornament.

This is a very common Hungarian pair meaning:

• one ... the other

So:

• az egyik porcelán dísztárgy = one is a porcelain ornament
• a másik utánzat = the other is an imitation

It is a fixed and very natural way to contrast two things.

Because in Hungarian, egyik and másik are very often used with the definite article when they mean one and the other out of a known pair.

So:

• az egyik = one of them / one
• a másik = the other

This is standard Hungarian usage. English learners often want to say just egyik and másik, but with this meaning the articles are normally there.

No. They are different:

• másik = the other
• második = second

So in your sentence:

• a másik utánzat = the other is an imitation

It does not mean the second is an imitation, even though English might sometimes use the second one in similar contexts.

It means something like porcelain decorative object / porcelain ornament.

Here:

• porcelán = porcelain
• dísztárgy = ornamental object / decorative object

dísztárgy itself is built from:

• dísz = decoration, ornament
• tárgy = object, item

In Hungarian, a noun like porcelán can stand in front of another noun and function a bit like an adjective, so porcelán dísztárgy is very natural.

Utánzat means imitation, copy, or replica.

In many contexts, it suggests that something is not the original. Depending on context, it can sound:

• neutral: a copy or replica
• slightly negative: an imitation, a fake-looking version

In this sentence, it contrasts with a real porcelán dísztárgy, so the meaning is basically an imitation.

The colon introduces an explanation or breakdown of the first statement.

So the structure is:

• Mindkettő szép: = Both are beautiful:
• az egyik ... , a másik ... = explanation of what each one is

It works much like English:

• Both are beautiful: one is a porcelain ornament, the other is an imitation.

Yes. Here are some natural alternatives:

• Mind a kettő szép: az egyik porcelán dísztárgy, a másik utánzat.
  Also means Both are beautiful...
  This is a slightly more separated form of mindkettő.

• Mindkét tárgy szép: az egyik porcelán dísztárgy, a másik utánzat.
  = Both objects are beautiful...
  Here the noun tárgy is said explicitly.

All of these are natural, but your original sentence is completely normal.

A rough guide:

• Mindkettő ≈ MIND-ket-tő
• szép ≈ sayp
• az egyik ≈ awz edj-ik
• porcelán ≈ por-tseh-laan
• dísztárgy ≈ dees-taarj
• a másik ≈ aw maa-shik
• utánzat ≈ oo-taan-zawt

A few useful sound notes:

• sz is pronounced like English s
• s is pronounced like English sh
• gy is a soft sound, somewhat like the dy in duke for many English speakers
• á is a longer open vowel, roughly like a in father

So dísztárgy and egyik are often the hardest words here for English speakers.