يطابق رقم اللوحة رقم الهيكل.

It is a verbal sentence with the order verb + subject + object.

• يطابق = matches
• رقم اللوحة = the plate number
• رقم الهيكل = the chassis number

So the structure is literally matches the plate number the chassis number, which becomes natural English as The plate number matches the chassis number.

Because both expressions are iḍāfa constructions, often called a construct phrase.

In an iḍāfa:

• the first noun usually does not take ال
• the second noun makes the whole phrase definite if it is definite

So:

• رقم اللوحة = the number of the plate = the plate number
• رقم الهيكل = the number of the chassis = the chassis number

That is why you do not say الرقم اللوحة here.

In fully vowelled MSA, the case endings show it clearly:

يُطابِقُ رَقْمُ اللَّوْحَةِ رَقْمَ الهَيْكَلِ

• رَقْمُ has -u because it is the subject (nominative)
• رَقْمَ has -a because it is the object (accusative)

In normal unvowelled writing, those endings are not shown, so learners usually rely on:

1. normal word order after the verb, and
2. context

After a verb, the first noun phrase is usually understood as the subject.

يطابق is the present-tense form of طابق. Here it means matches, corresponds to, or agrees with in the sense that two pieces of information are the same.

This verb is especially common in:

• official language
• document checking
• inspections
• record verification

So it fits very naturally in sentences about vehicle numbers and documents.

Because طابق / يطابق can take a direct object in MSA.

Arabic can say:

X يطابق Y

That is simply X matches Y.

So no extra word like with is needed here.

Because the head noun of the subject is رقم, and رقم is masculine singular.

That is what controls the verb, not اللوحة.

So even though لوحة is feminine, the subject as a whole is centered on رقم:

• رقم اللوحة = the number of the plate

Also, in a verbal sentence where the verb comes first, Arabic normally uses a singular verb before the subject. So يطابق is exactly what you would expect.

Yes. That is also grammatical.

It changes the order from:

• verb + subject + object

to:

• subject + verb + object

So both are possible:

• يطابق رقم اللوحة رقم الهيكل
• رقم اللوحة يطابق رقم الهيكل

The meaning is basically the same. The verb-first version sounds especially natural in formal written MSA.

By itself, لوحة can mean things like board, panel, sign, or plate.

In a vehicle context, it usually means the license plate or registration plate.

So رقم اللوحة means license plate number.

الهيكل literally means structure, frame, or skeleton.

In the context of vehicles, it refers to the chassis or body/frame.

So رقم الهيكل means chassis number, and in many practical contexts this corresponds to what English often calls the VIN.

With full case endings, it is:

يُطابِقُ رَقْمُ اللَّوْحَةِ رَقْمَ الهَيْكَلِ

A careful transliteration is:

yuṭābiqu raqmu l-lawḥati raqma l-haykali

In normal pause, many speakers do not pronounce the final short vowels fully, so what you hear in real life may sound a bit shorter than the fully vowelled form.