هذه المشكلة أسوأ.

Because مشكلة is a feminine singular noun in Arabic, and the demonstrative has to agree with it.

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

So:

• هذا الكتاب = this book
• هذه المشكلة = this problem

Even though problem is not feminine in English, مشكلة is grammatically feminine in Arabic.

A very common sign of a feminine noun in Arabic is the ـة ending, called tāʾ marbūṭa.

So مشكلة is feminine because it ends in ـة.

A few notes:

• In pause, it is usually pronounced as mushkila
• In connected speech with case endings, it can sound like mushkilatu / mushkilata / mushkilati depending on grammar

You do not need to translate the femininity literally into English. It is just part of the noun’s grammar.

In Arabic, the present tense of to be is usually not expressed in simple sentences like this.

So:

• هذه المشكلة أسوأ literally looks like this problem worse
• but it means This problem is worse

This is completely normal in Arabic.

If you wanted the past, then Arabic would use a verb:

• كانت هذه المشكلة أسوأ = This problem was worse

أسوأ means worse here. It is the comparative form of سيّئ (bad).

So the pattern is like this:

• سيّئ = bad
• أسوأ = worse / worst

This is not a regular English-style -er ending, of course. Arabic uses a special comparative/superlative form often called the elative.

Depending on context, أسوأ can mean:

• worse
• worse than ...
• sometimes the worst

In your sentence, the natural meaning is worse.

Because أسوأ here is not being used as a normal descriptive adjective like big, new, or difficult. It is being used as a predicate comparative: worse.

In this use, Arabic normally keeps it indefinite-looking:

• هذه المشكلة أسوأ = This problem is worse

Compare that with a normal adjective, which would usually match in definiteness:

• هذه المشكلة الكبيرة = this big problem

So أسوأ here is not matching with المشكلة the way an ordinary adjective would.

Arabic can leave the comparison understood from context, just like English sometimes can.

So هذه المشكلة أسوأ can mean:

• This problem is worse
• meaning: worse than the other one, worse than before, worse than expected, etc.

If you want to state the comparison explicitly, Arabic usually uses من for than:

• هذه المشكلة أسوأ من تلك = This problem is worse than that one
• هذا أسوأ من السابق = This is worse than the previous one

So the sentence is fine even without من, as long as the comparison is clear from context.

A careful MSA pronunciation is roughly:

hādhihi al-mushkilatu aswaʾ

In normal paused speech, you will often hear something closer to:

hādhihi al-mushkila aswaʾ

A few pronunciation points:

• هذه = hādhihi
• المشكلة = al-mushkila
• أسوأ = aswaʾ

The last sound in أسوأ is a hamza (ء), a glottal stop. So it ends with a little catch in the throat: as-waʾ.

In Modern Standard Arabic, the most standard and neutral way to say this problem is:

• هذه المشكلة

That is: demonstrative + definite noun

You may also encounter other wordings in some styles or dialects, but in MSA, هذه المشكلة is the normal form you should learn first.

So for a learner, the best model is:

• هذا الكتاب = this book
• هذه السيارة = this car
• هذه المشكلة = this problem

In this sentence, it functions as the predicate of the sentence: it tells you something about هذه المشكلة.

So the sentence has two main parts:

• هذه المشكلة = the subject-like part
• أسوأ = the predicate, telling us what it is like

You can think of it as similar to:

• الجو جميل = The weather is nice
• الطريق طويل = The road is long
• هذه المشكلة أسوأ = This problem is worse

So yes, it comes from an adjective meaning, but here it is specifically serving as the predicate of the sentence.

Yes, أسوأ can mean worse or worst, depending on the structure and context.

Examples:

• هذا أسوأ = This is worse
• هذا أسوأ حلّ = This is the worst solution or This is a worse solution, depending on context
• الأسوأ = the worst

In your sentence, the most natural reading is worse, not the worst.

In fully vocalized formal Arabic, yes.

The sentence could be read as:

هذه المشكلةُ أسوأُ

Why?

• المشكلةُ is the subject-like part and takes ḍamma
• أسوأُ is the predicate and also takes ḍamma

But in most everyday printed Arabic, these short vowels are not written, so you usually just see:

هذه المشكلة أسوأ

Learners should recognize that the grammar is still there even when the endings are omitted in writing.

مشكلة comes from a root related to difficulty / complication / being problematic, and it means problem.

You do not need the root to understand the sentence, but it can help vocabulary building. Related words include things connected with difficulty or complication.

For practical purposes, just remember:

• مشكلة = problem
• مشكلات or مشاكل = problems

Yes. Arabic often leaves things short when the context is clear. A fuller version might be:

• هذه المشكلة أسوأ من السابقة = This problem is worse than the previous one
• هذه المشكلة أسوأ من تلك المشكلة = This problem is worse than that problem

So your original sentence is a compact, natural sentence where the comparison is left implicit.