يأخذ مقدم الطلب رقم الانتظار للمعاملة.

A fully vocalized version is:

يَأْخُذُ مُقَدِّمُ الطَّلَبِ رَقْمَ الانْتِظَارِ لِلْمُعَامَلَةِ

A helpful pronunciation guide is:

yaʾkhudhu muqaddimu ṭ-ṭalabi raqma l-intiẓāri lil-muʿāmalati

In normal Arabic writing, those short vowels are usually omitted, so learners have to supply them from grammar and context.

Because verb–subject–object order is very common in Modern Standard Arabic.

So:

يأخذ مقدم الطلب رقم الانتظار
literally follows takes the applicant the waiting number

This is normal Arabic word order. You could also say:

مقدم الطلب يأخذ رقم الانتظار

That is also correct, but it feels more like The applicant takes... with extra focus on the subject.

مقدم الطلب is an iḍāfa construction, often called a construct phrase.

Literally, it means the submitter of the application/request:

• مقدم = submitter / presenter
• الطلب = the request / the application

Together, it functions as the applicant.

Also, مقدم is really pronounced مُقَدِّم here. In unvoweled Arabic writing, the short vowels and the shadda are usually not shown.

Because in an iḍāfa construction, the first noun usually does not take الـ.

So Arabic says:

مقدم الطلب

not:

المقدم الطلب

The definiteness comes from the second noun. Since الطلب is definite, the whole phrase مقدم الطلب becomes definite too: the applicant.

This is the same pattern: another iḍāfa.

• رقم = number
• الانتظار = the waiting

Together, رقم الانتظار means something like the waiting number or more naturally the queue number.

In an iḍāfa, the first noun does not take الـ, so رقم stays without الـ. Because الانتظار is definite, the whole phrase is definite.

للمعاملة means for the transaction / for the procedure / for the application process, depending on context.

The لِـ here means for. It tells you what the queue number is for.

So:

• رقم الانتظار = the queue number
• للمعاملة = for the procedure/service being handled

In office or government language, معاملة often means an official procedure, case, or paperwork process.

Because the preposition لِـ combines with الـ in writing.

So:

لِ + المعاملة = للمعاملة

This is completely regular in Arabic. The same thing happens in many other words, for example:

• للبيت = for the house
• للطالب = for the student

So للمعاملة is just the normal written form of for the procedure/transaction.

If you show the full grammar, the endings are:

يَأْخُذُ مُقَدِّمُ الطَّلَبِ رَقْمَ الانْتِظَارِ لِلْمُعَامَلَةِ

Here is why:

• يأخذُ: indicative verb
• مقدمُ: nominative, because it is the subject
• الطلبِ: genitive, because it is the second part of an iḍāfa
• رقمَ: accusative, because it is the direct object
• الانتظارِ: genitive, because it is the second part of an iḍāfa
• للمعاملةِ: genitive, because it comes after the preposition لِـ

In everyday written Arabic, these case endings are usually not written.

Because the verb comes from the root أ-خ-ذ, which means to take.

Its basic past-tense form is أخذ = he took, and its present-tense form is يأخذ = he takes. The hamza is part of the root, so it stays in the spelling.

In this sentence, يأخذ is third person masculine singular, which matches مقدم الطلب.