Numărul de referință apare în reclamație.

Because -ul is the Romanian definite article attached to the end of the noun.

• număr = a number
• numărul = the number

Romanian usually puts the at the end of the noun instead of using a separate word like English does.

So:

• numărul de referință = the reference number

de referință means reference in the sense of used for identification.

Literally, Romanian often uses:

• noun + de + noun

where English might use:

• noun + noun

So:

• număr de referință = literally number of reference
• natural English: reference number

This pattern is very common in Romanian:

• carte de vizită = business card
• sală de clasă = classroom
• număr de telefon = phone number

Because in numărul de referință, the noun referință is part of a fixed descriptive phrase, not a separate noun being made definite.

So Romanian marks the main noun as definite:

• numărul = the number

but leaves the classifier phrase general:

• de referință = for reference / reference-type

Compare:

• un număr de referință = a reference number
• numărul de referință = the reference number

You normally would not say numărul de referința with another article on referință here.

apare comes from the verb a apărea, meaning to appear, to show up, or sometimes to be found/listed depending on context.

Here:

• apare = appears

It is the 3rd person singular, present tense form, matching numărul:

• numărul apare = the number appears

A few present-tense forms of a apărea:

• eu apar = I appear
• tu apari = you appear
• el/ea apare = he/she/it appears
• ei/ele apar = they appear

No. Just like English appears, Romanian apare can be used more broadly.

It can mean:

• shows up
• is present
• appears in writing
• is listed

So in this sentence, it likely means something like:

• The reference number appears in the complaint
• The reference number is shown in the complaint
• The reference number is listed in the complaint

Good question. Without the article, reclamație is formally indefinite:

• reclamație = a complaint
• reclamația = the complaint

So strictly speaking:

• în reclamație = in a complaint
• în reclamația = in the complaint

However, in bureaucratic or administrative Romanian, an indefinite-looking form can sometimes sound more general or document-related, almost like on the complaint form / in the complaint text.

If you want to refer to one specific complaint already known in the conversation, în reclamația would usually be the clearer form.

Here it means complaint.

This is a very useful distinction:

• reclamație = complaint, claim
• reclamă = advertisement

So don’t confuse:

• am făcut o reclamație = I made/filed a complaint
• am văzut o reclamă = I saw an advertisement

Even though they look related, they mean different things in modern Romanian.

The sentence uses a very normal Romanian word order:

• Numărul de referință = subject
• apare = verb
• în reclamație = prepositional phrase

So:

• Numărul de referință apare în reclamație.

Romanian word order is fairly flexible, though. You could also say:

• În reclamație apare numărul de referință.

That would put more focus on where it appears.

A rough pronunciation guide is:

Nu-muh-rul de reh-feh-RIN-tsuh a-PA-reh in reh-klah-ma-TSEE-eh

A few key sounds:

• ă in numărul = a short neutral vowel, like the a in sofa
• ț in referință = ts
• ție in reclamație sounds like tsee-eh

Word by word:

• Numărul → NU-muh-rul
• de → deh
• referință → reh-feh-RIN-tsuh
• apare → a-PA-reh
• în → roughly în with a central vowel, not a full English in
• reclamație → reh-klah-ma-TSEE-eh

Romanian usually does not need a subject pronoun unless you want emphasis or contrast.

Because numărul de referință is already the subject, there is no need for el.

Compare:

• Numărul de referință apare... = The reference number appears...
• El apare... = It appears...

Romanian often leaves pronouns out when the subject is already clear.

It would be:

Numerele de referință apar în reclamații.

Breakdown:

• numărul → numerele = the numbers
• apare → apar = appear
• reclamație → reclamații = complaints

So:

• Numerele de referință apar în reclamații.
• The reference numbers appear in complaints.

Notice that de referință stays the same.

Yes, it is very useful to memorize it as a chunk.

You will often see:

• număr de referință = reference number
• punct de referință = reference point
• sistem de referință = reference system
• cadru de referință = framework of reference / reference framework

Learning de referință as a set phrase will help you recognize similar structures more quickly.