القطعة الفخارية ماتحرقتش في فرن الفخار.

Because Arabic normally puts adjectives after the noun they describe.

• القطعة = the piece
• الفخارية = ceramic / pottery / earthenware

So القطعة الفخارية is literally the piece the-ceramic, which in natural English becomes the ceramic piece.

In Arabic, adjectives agree with the noun in definiteness as well as gender and number.

So:

• قطعة فخارية = a ceramic piece
• القطعة الفخارية = the ceramic piece

Since القطعة is definite, the adjective الفخارية also has to be definite.

It comes from فخار, which means pottery / earthenware / ceramics.

The adjective is formed with the common Arabic adjectival ending -ي; because the noun it describes is feminine, it appears here as -ية:

• فخار = pottery
• فخاري = ceramic / made of pottery
• فخارية = feminine form of that adjective

So القطعة الفخارية means the ceramic piece or the pottery piece.

Because قطعة is a feminine singular noun, and the adjective has to match it.

Arabic adjectives agree with the noun in:

• gender
• number
• definiteness

So with feminine singular قطعة, you get feminine singular فخارية.

This is the very common Egyptian Arabic negation pattern ما ... ش wrapped around the verb.

So you can think of it as:

• ما + تحرقت + ش

This pattern is a hallmark of spoken Egyptian Arabic. It is used with many verbs, for example:

• ماعرفش = I don’t know
• ماجاش = he didn’t come
• ماتحرقتش = it didn’t get burned / it wasn’t burned

That -ت shows feminine singular in the past tense.

Since the subject is القطعة (the piece), which is feminine singular, the verb matches it:

• تحرقت = it got burned / she got burned depending on context

Here it refers to the feminine noun القطعة.

In this sentence, it functions more like got burned or was burned than like burned something.

That is very normal in Arabic. Egyptian often uses a verb form that describes what happened to the subject, where English might prefer a passive.

So the idea is not that the piece burned something else, but that the piece underwent burning.

This is a noun-to-noun construction called iḍāfa.

Literally, it is something like:

• فرن = oven / kiln
• الفخار = pottery / ceramics

So فرن الفخار is literally the kiln of pottery, which we would naturally render in English as the pottery kiln.

Arabic often uses this kind of structure where English might use a noun plus adjective.

Because in an iḍāfa construction, the first noun normally does not take ال.

So:

• فرن الفخار is correct
• الفرن الفخار is not how this structure works

The first noun is linked directly to the second noun, and the definiteness of the whole phrase is controlled by the second part.

Because the second noun in an iḍāfa is where definiteness is shown.

So when you have فرن الفخار, the الـ on الفخار helps make the whole phrase definite. This is why Arabic can have a phrase where the first noun has no الـ, but the whole expression is still definite.

A rough pronunciation would be:

el-ʔeṭʿa el-faḫḫāriyya ma-taḥraʔitš fi forn el-faḫḫār

A few useful pronunciation notes:

• ق in القطعة is often pronounced as a glottal stop in Cairene Egyptian.
• خ is the raspy kh sound, like German Bach.
• ع in قطعة is a deep throat sound with no exact English equivalent.
• ش at the end of ماتحرقتش is the final part of the Egyptian negative.

It is clearly Egyptian Arabic, mainly because of the negation ما...ش.

That pattern is typical of spoken Egyptian and is not used in Modern Standard Arabic. A more formal MSA-style version would be something like:

القطعة الفخارية لم تحترق في فرن الفخار

So this sentence is a good example of everyday Egyptian grammar rather than formal written Arabic.