فيه حل للمشكلة دي؟

A common Egyptian pronunciation is:

fīh ḥall lel-moshkela دي؟

You may also see it written as:

• fih hall lel-moshkela di?
• fīh ḥall lil-mushkila di?

A few notes:

• فيه = fīh or sometimes just fī
• حل = ḥall, with a strong h sound from deep in the throat
• للمشكلة is often pronounced lel-moshkela in Egyptian speech
• دي = di

So the whole sentence sounds roughly like:

feeh hall lel-moshkela dee?

Here فيه means there is / is there.

In Egyptian Arabic, فيه is very commonly used to express existence:

• فيه وقت = There is time
• فيه مشكلة = There is a problem
• فيه حل؟ = Is there a solution?

So in your sentence, فيه is not the preposition in him/it in a literal sense. It functions as an existential expression: there is / there are.

Because Egyptian Arabic often uses فيه to begin sentences that mean there is / are there.

English says:

• Is there a solution to this problem?

Egyptian Arabic naturally says something like:

• There-is solution for-the-problem this?

So starting with فيه is the normal way to ask whether something exists.

In Egyptian Arabic, yes/no questions are very often made just by intonation.

So:

• فيه حل للمشكلة دي. = There is a solution to this problem.
• فيه حل للمشكلة دي؟ = Is there a solution to this problem?

The words stay the same; your voice rises at the end.

Unlike Modern Standard Arabic, Egyptian usually does not need هل in everyday speech.

Because the sentence means Is there a solution..., not Is there the solution...

In Arabic, حل without ال means a solution / any solution.

• حل = a solution
• الحل = the solution

So:

• فيه حل للمشكلة دي؟ = Is there a solution to this problem?
• فيه الحل للمشكلة دي؟ would sound different and much less natural here, because it suggests a specific known solution.

The لـ here means for / to.

So:

• حل للمشكلة literally means a solution for the problem

That is how Arabic commonly expresses a solution to a problem.

Breakdown:

• لـ = for / to
• المشكلة = the problem
• للمشكلة = for the problem

Because لـ is attached directly to المشكلة, they become one written word: للمشكلة.

Yes, دي means this for a feminine noun in Egyptian Arabic.

And in Egyptian, demonstratives like دي usually come after the noun:

• المشكلة دي = this problem

That is different from English, where this comes before the noun.

So:

• المشكلة دي literally = the problem this
• natural English = this problem

Because مشكلة is a feminine noun.

In Egyptian Arabic:

• ده = this for masculine nouns
• دي = this for feminine nouns

Examples:

• الكتاب ده = this book
• المشكلة دي = this problem

So دي agrees with مشكلة.

That is normal in Arabic.

In Egyptian Arabic, when you say this/that + noun, the noun is usually definite, so you get:

• المشكلة دي = literally the problem this
• natural English = this problem

This is just standard Arabic structure. You do not usually say مشكلة دي.

It is clearly Egyptian colloquial.

The most Egyptian-looking part is دي.

In Modern Standard Arabic, you would say:

• هل هناك حل لهذه المشكلة؟ or
• أهناك حل لهذه المشكلة؟

Key differences:

• Egyptian: دي
• MSA: هذه

Also, فيه as there is is very common in spoken dialects, while MSA often uses هناك in this kind of sentence.

You can, and people will understand you, but it sounds less naturally Egyptian and more mixed or formal.

In everyday Egyptian Arabic, the usual version is simply:

• فيه حل للمشكلة دي؟

Adding هل makes it sound more like you are mixing in Standard Arabic.

So if your goal is natural spoken Egyptian, it is better to leave هل out.

Because Arabic often does not use a separate present-tense verb to be the way English does.

English says:

• Is there a solution...?

Egyptian Arabic uses فيه to express existence, so no extra word like is is needed.

This is very normal in Arabic. The sentence is complete without a separate present-tense be verb.

A very common negative version in Egyptian is:

• مفيش حل للمشكلة دي. = There is no solution to this problem.

Here:

• مفيش = there isn't / there is no

So you get the pair:

• فيه حل للمشكلة دي؟ = Is there a solution to this problem?
• مفيش حل للمشكلة دي. = There is no solution to this problem.

Yes. A few natural alternatives are:

• فيه حل للمشكلة دي ولا لأ؟
  = Is there a solution to this problem or not?

• مفيش حل للمشكلة دي؟
  = depending on tone, Isn’t there a solution to this problem?

• ممكن نلاقي حل للمشكلة دي؟
  = Can we find a solution to this problem?

But your original sentence, فيه حل للمشكلة دي؟, is already very natural and common.