الغرفة المفردة والغرفة المزدوجة مكيفتان.

Because this is a present-tense nominal sentence in Arabic. In sentences like this, Arabic usually does not use a separate present-tense verb meaning is/are.

So:

• الغرفة المفردة والغرفة المزدوجة مكيفتان = The single room and the double room are air-conditioned

There is no written word for are, but the meaning is understood.

If you wanted a past-tense version, then Arabic would use a verb, for example كانتا for were with two feminine things.

Because the sentence is talking about exactly two things:

• الغرفة المفردة = the single room
• الغرفة المزدوجة = the double room

Arabic has a special grammatical number for two, called the dual.

So instead of using a plural predicate, Arabic uses the dual:

• مكيفتان = two air-conditioned (feminine things)

If there were three or more rooms, you would use a plural form instead.

Because both nouns it refers to are غرفة, and غرفة is a feminine noun in Arabic.

That means words agreeing with it must also be feminine:

• غرفة مفردة — feminine
• غرفة مزدوجة — feminine
• مكيفتان — feminine dual

So the sentence is not just dual; it is specifically feminine dual.

The ending -تان shows feminine dual in the nominative case.

So مكيفتان means something like:

• two air-conditioned ones
  or more naturally:
• are air-conditioned (when used as the predicate here)

A fuller grammatical form with case vowels is مكيفتانِ.

You may also see مكيفتينِ in other contexts. That form is used in the accusative or genitive, not here.

Because مكيفتان is the predicate of the sentence, not an adjective directly attached to a noun.

Compare these two patterns:

1. Attributive adjective:

   • الغرفة المكيفة = the air-conditioned room
     Here the adjective describes the noun directly, so it matches it in definiteness and takes الـ.

2. Predicate adjective:

   • الغرفة مكيفة = the room is air-conditioned
     Here مكيفة is the predicate, so it is normally indefinite.

In your sentence, مكيفتان is the predicate for the two rooms, so it does not take الـ.

Because in Arabic, adjectives usually come after the noun they describe.

So:

• الغرفة المفردة = the single room
• الغرفة المزدوجة = the double room

This is the normal Arabic order:

• noun + adjective

Also, Arabic adjectives must agree with the noun in:

• gender
• number
• definiteness
• case

That is why both are definite:

• الغرفة المفردة
• الغرفة المزدوجة

not just غرفة المفردة or الغرفة مفردة in this specific noun-phrase use.

Repeating الغرفة makes it clear that we are talking about two separate rooms:

• الغرفة المفردة = one room
• الغرفة المزدوجة = another room

If you said الغرفة المفردة والمزدوجة, it could sound like one room being described by two adjectives, which would be confusing.

So Arabic often repeats the noun to make the coordination clear:

• الغرفة المفردة والغرفة المزدوجة

This clearly means the single room and the double room.

Grammatically, it is best understood here as a predicate adjective.

The base word مكيف means air-conditioned. It comes from a participial form, but in sentences like this it works very much like an adjective:

• الغرفة مكيفة = The room is air-conditioned
• الغرفتان مكيفتان = The two rooms are air-conditioned

So in this sentence, مكيفتان is the khabar (predicate) of the nominal sentence.

A careful pronunciation is approximately:

al-ghurfatu al-mufradatu wal-ghurfatu al-muzdawijatu mukayyafatāni

In normal pause, many final short vowels are not pronounced, so you may hear something closer to:

al-ghurfa al-mufrada wal-ghurfa al-muzdawija mukayyafatān

A few pronunciation notes:

• غ in الغرفة is a deep throaty sound, often compared loosely to a French or German r
• الـ before غ is pronounced normally, because غ is a moon letter, not a sun letter
• و joins smoothly to the next word: wa-l-ghرفة

مفردة here means single in the sense used for hotel rooms or room types.

So:

• غرفة مفردة = single room
• غرفة واحدة = literally one room

Those are not always the same idea.

In hotel vocabulary:

• مفردة contrasts with مزدوجة
• single contrasts with double

So المفردة is the natural word here, not الواحدة.

Yes. That is a good way to understand it.

The structure is:

• الغرفة المفردة = first subject element
• والغرفة المزدوجة = second subject element joined by و
• مكيفتان = predicate for both together

So the subject is effectively a coordinated pair of nouns, and the predicate agrees with that pair in being:

• dual
• feminine
• nominative

That is why مكيفتان is exactly the form you would expect here.