حافة الحوض جنب المي الضحلة زلقة.

This is an iḍāfa construction, often called a possessive or of construction.

• حافة الحوض literally means edge of the pool/basin
• In an iḍāfa, the first noun usually does not take ال
• The second noun can be definite, and that makes the whole phrase definite

So:

• حافة حوض = an edge of a pool
• حافة الحوض = the edge of the pool

Even though حافة has no ال, the whole phrase is still definite because الحوض is definite.

Because حافة ends in ة (taa marbuuTa), and in connected speech that ة is often pronounced as -t when the word is followed by another word in an iḍāfa.

So:

• by itself: حافة → roughly ḥāfe / ḥāffe
• in iḍāfa: حافة الحوض → roughly ḥāfet il-ḥōḍ

That is very normal in Arabic. English speakers often notice the written ة but are surprised when it becomes a real t sound in phrases like this.

جنب here means next to, beside, or near.

So جنب المي الضحلة means:

• next to the shallow water
• by the shallow water
• near the shallow water

In this sentence, that phrase is describing which edge we are talking about. So the structure is basically:

• حافة الحوض جنب المي الضحلة = the edge of the pool near the shallow water
• زلقة = is slippery

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

So:

• المي الضحلة = the shallow water

not the English-style order shallow water.

Also, the adjective has to match the noun in things like:

• definiteness
• gender
• number

Here:

• المي is definite, so الضحلة is also definite
• المي is treated as feminine singular in Levantine, so الضحلة is feminine singular too

That is why الضحلة looks the way it does.

Because it agrees with the subject, and the head noun of the subject is حافة, which is feminine singular.

The subject is not الحوض. The main noun is حافة:

• حافة الحوض = the edge of the pool

Since حافة is feminine singular, the predicate adjective is also feminine singular:

• زلقة = slippery (feminine singular)

If the noun were masculine singular, you would expect something like زلق instead.

Because in a sentence like this, the predicate adjective is usually indefinite.

This is a very common Arabic pattern:

• الباب مفتوح = the door is open
• الأرض مبلولة = the ground is wet
• حافة الحوض ... زلقة = the edge of the pool ... is slippery

So:

• the subject is definite: حافة الحوض
• the describing word after it is indefinite: زلقة

That is the normal way to say is slippery in the present tense.

In Arabic, especially in the present tense, you usually do not say a separate word for is/am/are.

So Arabic often says:

• حافة الحوض زلقة
• literally: the edge of the pool slippery
• natural English: the edge of the pool is slippery

This is called a nominal sentence.

If you wanted past or future, then Arabic would usually use a verb such as كان or a future form:

• كانت زلقة = it was slippery
• رح تكون زلقة = it will be slippery

But in the present, no separate is is needed.

Because ض is a sun letter, so the ل of ال assimilates to it in pronunciation.

So الضحلة is pronounced more like:

• iḍ-ḍaḥle / eḍ-ḍaḥle

not:

• il-daḥle

This happens with all sun letters in Arabic. In writing, the ال stays the same, but in speech the l sound blends into the next consonant.

So a rough pronunciation of the whole sentence could be:

• ḥāfet il-ḥōḍ janb il-mayy iḍ-ḍaḥle zalʔa

Pronunciation varies a bit by region, but that is the basic idea.

Most naturally, it describes which edge.

So the sentence is best understood as:

• The edge of the pool near the shallow water is slippery

rather than:

• The edge of the pool is slippery near the shallow water

In other words, جنب المي الضحلة attaches to the noun phrase حافة الحوض, helping identify the location of that edge.

المي is a very common Levantine colloquial word for water. In Modern Standard Arabic, you would more often see الماء.

So:

• Levantine: المي
• MSA: الماء

As for الحوض, it is a real Arabic word and can mean different things depending on context, such as:

• pool
• basin
• sink
• tub
• sometimes even pond

In this sentence, because of المي الضحلة (the shallow water), the most natural interpretation is probably pool.