هذا حل محتمل.

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

So:

• هذا حل محتمل = This is a possible solution

This is called a nominal sentence. Arabic often just places the subject and predicate next to each other.

Compare:

• هذا حل محتمل = This is a possible solution
• كان هذا حلًّا محتملًا = This was a possible solution
• سيكون هذا حلًّا محتملًا = This will be a possible solution

So the missing is is completely normal.

هذا means this and is the masculine singular demonstrative in MSA.

It is used here because حل (solution) is a masculine noun.

So:

• هذا = this (masculine singular)
• هذه = this (feminine singular)

For example:

• هذا كتاب = This is a book
• هذه فكرة = This is an idea

Since حل is masculine, هذا is the correct form.

In this sentence, هذا is not simply an adjective-like word attached to حل. The whole sentence means:

• هذا = this
• حل محتمل = a possible solution

So the structure is:

• subject: هذا = this
• predicate: حل محتمل = a possible solution

That is why the sentence means This is a possible solution, not just this possible solution.

If you wanted this possible solution as a noun phrase, you would normally say:

• هذا الحل المحتمل

That phrase is different in structure and meaning.

Because the phrase means a possible solution, not the possible solution.

In Arabic:

• حل محتمل = a possible solution (indefinite)
• الحل المحتمل = the possible solution (definite)

Since the English meaning uses a, Arabic leaves both the noun and adjective indefinite.

This is also why the sentence is not:

• هذا الحل المحتمل

because that would usually mean this possible solution or this is the possible solution, depending on context.

محتمل is an adjective describing حل.

So:

• حل = solution
• محتمل = possible

Arabic adjectives usually come after the noun they describe, unlike English.

So Arabic says:

• حل محتمل
• literally: solution possible

not:

• محتمل حل

Also, the adjective agrees with the noun in:

• gender
• number
• definiteness
• case

Here both are:

• masculine
• singular
• indefinite
• nominative

The fully vocalized form is:

• هٰذا حَلٌّ مُحْتَمَلٌ

A few details:

• هذا is a fixed form, so it does not take a normal visible case ending here.
• حلٌّ has tanwīn ḍamm because it is an indefinite nominative predicate.
• محتملٌ also has tanwīn ḍamm because it is an adjective matching حلٌّ.

In normal Arabic writing, these short vowels are usually omitted, so you normally just see:

• هذا حل محتمل

Yes. The word حل is normally pronounced ḥall, with a doubled l sound.

In full vocalization it is:

• حَلّ

Important pronunciation points:

• ح is a deep, breathy ḥ sound, not the ordinary English h
• لّ is doubled because of the shadda

So it is roughly:

• ḥall

not just ḥal.

In the full sentence, a careful reading would be something like:

• hādhā ḥallun muḥtamalun

In pause, the final short endings are often not pronounced:

• hādhā ḥall muḥtamal

هذا is pronounced hādhā.

The letter ذ is pronounced like the th in this, not like z and not like the th in think.

So:

• ه = h
• ا = long ā
• ذ = th as in this
• ا = long ā

That gives:

• hā-dhā

English speakers often mispronounce it as haza or hatha, but in MSA the standard pronunciation is hādhā.

محتمل comes from the root ح م ل. In modern usage, it often means:

• possible
• probable
• potential, depending on context

In this sentence, possible is the natural meaning.

It is related to the noun:

• احتمال = possibility / probability

So you may later see related expressions such as:

• هناك احتمال = There is a possibility
• احتمال كبير = a strong possibility

So learning محتمل together with احتمال is very useful.

Yes, but هو is not necessary here.

The simplest and most natural sentence is:

• هذا حل محتمل

Adding هو can give extra emphasis or clarity in some contexts:

• هذا هو الحل = This is the solution
• هذا هو السبب = This is the reason

With your sentence, هذا حل محتمل is already complete and normal. A learner should be comfortable using it without هو.