هذه مشكلة حقيقية.

Because مشكلة is a feminine noun, and the demonstrative has to match it.

• هذا = this for masculine nouns
• هذه = this for feminine nouns

Since مشكلة ends in ـة (tāʾ marbūṭa), it is feminine, so هذه is the correct form.

هذه is a demonstrative pronoun, meaning this.

In this sentence, it points to something near the speaker:

• هذه = this

So the sentence structure is basically:

• هذه = this
• مشكلة حقيقية = a real problem

Together: This is a real problem.

In Arabic, the verb to be is usually not stated in the present tense.

So English:

• This is a real problem

Arabic:

• هذه مشكلة حقيقية

There is no separate word for is, but it is understood automatically.

If you were talking about the past or future, Arabic would normally use a form of كان or another verb:

• كانت هذه مشكلة حقيقية = This was a real problem

Because the sentence means a real problem, not the real problem.

• مشكلة = a problem
• المشكلة = the problem

So:

• هذه مشكلة حقيقية = This is a real problem
• هذه المشكلة الحقيقية would mean something like This is the real problem or This real problem, depending on context

In Arabic, definiteness matters a lot, and adjectives must match it too.

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

So:

• مشكلة = problem
• حقيقية = real

Arabic order:

• problem real

English order:

• real problem

This is one of the most basic word-order differences between English and Arabic.

Because Arabic adjectives must agree with the noun they describe.

They usually match in:

• gender
• number
• definiteness
• case

Here:

• مشكلة is feminine singular indefinite
• so حقيقية must also be feminine singular indefinite

That is why you get:

• مشكلة حقيقية

and not:

• مشكلة حقيقي

The final ـة is called tāʾ marbūṭa. It often marks a noun or adjective as feminine.

So:

• مشكلة is feminine
• حقيقية is feminine

In pause, it is usually pronounced like -a:

• mushkila
• ḥaqīqiyya

In fully inflected reading, the ending may sound like -tun or -tun with tanwīn, depending on the word and case:

• mushkilatun
• ḥaqīqiyyatun

Those endings are tanwīn (nunation), and here they mark the words as indefinite and nominative.

A fully vocalized version is:

• هٰذِهِ مُشْكِلَةٌ حَقِيقِيَّةٌ

Why nominative? Because this is a simple nominal sentence:

• هذه = subject/topic
• مشكلةٌ = predicate
• حقيقيةٌ = adjective describing the predicate noun

In careful MSA pronunciation, you may hear:

• hādhihi mushkilatun ḥaqīqiyyatun

But in normal pause, many speakers drop the final case endings:

• hādhihi mushkila ḥaqīqiyya

In MSA, هذه is pronounced hādhihi.

A rough breakdown:

• hā = long aa
• dhi = like dh in this
• hi = short hi

So: hā-dhi-hi

Some learners are surprised because the spelling is short but the pronunciation has three syllables.

Here it is clearly an adjective meaning real, genuine, or actual.

It comes from the root related to truth/reality and is connected to the noun:

• حقيقة = truth, reality

So:

• حقيقي = real (masculine)
• حقيقية = real (feminine)

In this sentence, it describes مشكلة, so it is an adjective.

Yes, that is a very useful beginner way to see it.

Word-for-word:

• هذه = this
• مشكلة = problem
• حقيقية = real

Natural English:

• This is a real problem.

That kind of literal breakdown is often helpful when getting used to Arabic word order.

Not as written.

هذه مشكلة حقيقية most naturally means:

• This is a real problem

If you want This problem is real, you would normally say:

• هذه المشكلة حقيقية

Why? Because then هذه المشكلة = this problem and حقيقية = is real

So the presence or absence of الـ changes the structure and meaning.

The adjective حقيقية agrees with مشكلة in all the expected ways:

• Gender: both feminine
• Number: both singular
• Definiteness: both indefinite
• Case: both nominative in this sentence

That is a core rule of Arabic adjectives. If one changes, the other usually changes too.

For example:

• مشكلة حقيقية = a real problem
• المشكلة الحقيقية = the real problem

So Arabic is very strict about adjective agreement compared with English.