ننقل صناديق الكرتون حتى تصبح غرفة النوم فارغة.

This is a broken plural, which is very common in Arabic. Instead of adding a regular ending, the internal shape of the word changes:

• صندوق = box
• صناديق = boxes

English speakers often expect a simple ending like -s, but Arabic often forms plurals this way.

Because this is an iḍāfa construction, often called a construct phrase. In an iḍāfa:

• the first noun does not take ال
• the second noun can take ال
• the whole phrase gets its definiteness from the second noun

So صناديق الكرتون means something like cardboard boxes or the cardboard boxes, depending on context. Putting ال on the first noun here would be ungrammatical in standard Arabic.

No. In this sentence, الكرتون means cardboard. So صناديق الكرتون means cardboard boxes.

This can confuse English speakers because the word looks similar to cartoon. In some everyday speech, كرتون can refer to cartoons or animation, but in this phrase the meaning is clearly cardboard.

Here حتى means until, or more loosely so that in the end. It introduces the result or endpoint of the action.

So the idea is: the moving continues until the bedroom reaches the state of being empty.

تصبح comes from the verb أصبح / يصبح, which means to become. After حتى, Arabic often uses the imperfect verb to show a goal, result, or endpoint.

In fully vocalized Arabic, it would normally be تُصبِحَ, with the subjunctive ending after حتى. In normal unvocalized writing, you usually just see تصبح.

Because the main noun in غرفة النوم is غرفة, and غرفة is feminine. In an iḍāfa, agreement follows the first noun, which is the head noun.

So:

• غرفة = room, feminine
• النوم = sleep
• غرفة النوم = bedroom

That is why the verb is تصبح and the adjective is فارغة: both agree with غرفة, not with النوم.

This is another iḍāfa construction. Literally, it means room of sleep:

• غرفة = room
• النوم = sleep

Arabic often builds compound nouns this way. So غرفة النوم is the normal way to say the bedroom.

It is feminine because it describes غرفة, and غرفة is a feminine noun. Arabic adjectives must agree with the noun they describe in gender and number.

So:

• فارغ = empty, masculine
• فارغة = empty, feminine

Since the bedroom is expressed by غرفة النوم, and the head noun غرفة is feminine, فارغة is the correct form.

Because فارغة is not being used as an attributive adjective like the empty bedroom. It is the predicate of تصبح, meaning it tells you what state the bedroom becomes.

Compare:

• غرفة النوم فارغة = the bedroom is empty
• غرفة النوم الفارغة = the empty bedroom

So in your sentence, فارغة is indefinite because it functions as the predicate, not as part of a noun phrase.

A fully vocalized version would be:

نَنْقُلُ صَنَادِيقَ الْكَرْتُونِ حَتَّى تُصْبِحَ غُرْفَةُ النَّوْمِ فَارِغَةً

A quick breakdown:

• نَنْقُلُ = we move
• صَنَادِيقَ = boxes, direct object
• الْكَرْتُونِ = of cardboard
• حَتَّى = until
• تُصْبِحَ = becomes, in the subjunctive after حتى
• غُرْفَةُ النَّوْمِ = the bedroom
• فَارِغَةً = empty

So this sentence is a nice example of:

• an implied subject in the verb
• two iḍāfa constructions
• agreement with a feminine noun
• حتى followed by a subjunctive verb