تعمل المصابيح الخلفية.

Because this is a verbal sentence in Arabic. A very common Arabic pattern is:

verb + subject + modifiers

So here the structure is:

تعمل = works / is working
المصابيح = the lights
الخلفية = rear / back

English usually prefers The rear lights work, but Arabic often prefers Work the rear lights in its normal word order.

تعمل is the present/imperfect tense form of the verb عَمِلَ / يَعْمَلُ.

Here it means works, is working, or functions.

In this sentence, it is 3rd person feminine singular.

This is one of the most important grammar points in Arabic:

Non-human plurals are usually treated as feminine singular for agreement in Modern Standard Arabic.

So even though المصابيح is plural, the verb is still feminine singular:

• تعمل
• not a plural verb form

This is normal Arabic grammar, not a mistake.

المصابيح is the plural of مِصْباح.

• مِصْباح = lamp / light
• المصابيح = the lamps / the lights

This plural is a broken plural, which means the inside pattern of the word changes rather than just adding a regular ending.

Because it is an adjective describing المصابيح, and with non-human plural nouns, adjectives also usually appear in the feminine singular.

So:

• المصابيح = plural
• الخلفية = feminine singular adjective

That may feel strange to an English speaker, but it is standard Arabic agreement for non-human plurals.

Because the adjective must match the noun in definiteness.

So if the noun is definite:

• المصابيح = the lights

then the adjective must also be definite:

• الخلفية = the rear

Together, that gives:

المصابيح الخلفية = the rear lights

In Arabic, adjective phrases usually match in:

• definiteness
• gender
• number
• case

Here الخلفية means rear, back, or rear-side.

So المصابيح الخلفية means the rear lights or the taillights depending on context.

In other contexts, خلفية can also mean background, but here it is clearly an adjective meaning rear/back.

It would be:

تَعْمَلُ الْمَصَابِيحُ الْخَلْفِيَّةُ

Those endings show the grammar clearly:

• تعملُ = present tense verb
• المصابيحُ = subject in the nominative
• الخلفيةُ = adjective matching the subject

In normal unvowelled writing, these short vowels are usually omitted.

A careful reading would be:

taʿmalu al-maṣābīḥu al-khalfiyyatu

In pause, Arabic often drops the final short vowels, so you may hear something closer to:

taʿmal al-maṣābīḥ al-khalfiyya

A few pronunciation notes:

• ع is the deep throat sound in taʿmal
• خ is like the ch in Scottish loch or German Bach
• ص is a heavy/emphatic s

Yes. That is also possible.

• تعمل المصابيح الخلفية = verb-first
• المصابيح الخلفية تعمل = subject-first

Both are grammatical. The subject-first version can sound more topical or emphatic, like The rear lights are working.

Because المصابيح is a non-human plural, the verb still commonly stays feminine singular: تعمل.