Yengem yaptığı sütlacı küçük kaselere paylaştırdı, herkes çok beğendi.

Yengem means my sister-in-law in this sentence.

It is:

• yenge = sister-in-law
• -m = my

So yengem literally means my yenge.

A small cultural note: yenge can be used a bit more broadly in Turkish than sister-in-law is in English, depending on family and social context. But here, my sister-in-law is the natural translation.

Yaptığı is a relative-clause form built from yapmak = to make/do.

It breaks down like this:

• yap- = do/make
• -dık / -dik / -duk / -dük = a participle/relative-clause ending
• -ı / -i / -u / -ü = 3rd person possessive agreement

So yaptığı means something like:

• that he/she made
• the one he/she made

In yaptığı sütlaç, the meaning is the rice pudding that she made.

This is a very common Turkish structure:

• yaptığım yemek = the food that I made
• yaptığın pasta = the cake that you made
• yaptığı sütlaç = the rice pudding that he/she made

A learner often expects yengemin yaptığı sütlaç, and that is absolutely a very clear, fully explicit version.

• Yengemin yaptığı sütlaç = the rice pudding that my sister-in-law made

In your sentence, yengem already appears as the main subject, so the person who made the rice pudding is understood from context. Turkish often leaves things implicit when they are clear.

So:

• Yengem yaptığı sütlacı... = natural when the listener can easily understand that she is the one who made it
• Yengemin yaptığı sütlacı... = more explicit

Both are understandable, but the sentence you were given is more compact and conversational.

This is an important grammar point.

Use -an / -en when the noun being described is the subject of the action:

• yapan kadın = the woman who does/makes it
  The woman is the one doing the action.

Use -dık / -dik / -duk / -dük forms like yaptığı when the noun being described is the object of the action:

• yaptığı sütlaç = the rice pudding that she made
  The rice pudding is what she made, not the thing doing the action.

So:

• yapan = who does/makes
• yaptığı = that he/she did/made

Because it is the definite direct object, so it takes the accusative ending.

Base noun:

• sütlaç = rice pudding

Accusative form:

• sütlacı = the rice pudding

Two things happen:

1. It takes the accusative suffix.
2. Final ç changes to c before a vowel.

So:

• sütlaç → sütlacı

Why accusative? Because this is a specific, known rice pudding: the one she made.

Compare:

• Sütlaç yaptı. = She made rice pudding.
  More general / nonspecific.
• Sütlacı paylaştırdı. = She portioned out the rice pudding.
  Specific.

Kaselere is:

• kase = bowl
• -ler / -lar = plural
• -e / -a = dative, meaning to or into

So küçük kaselere means into small bowls or to small bowls.

That fits the verb paylaştırmak, because the dessert is being divided and put into separate bowls.

So:

• küçük kaselere paylaştırdı = she portioned/distributed it into small bowls

In Turkish, adjectives do not agree with the noun in number or case.

So even though kaselere is plural and dative, the adjective stays the same:

• küçük kase = small bowl
• küçük kaseler = small bowls
• küçük kaselere = to/into small bowls

The adjective küçük never changes here.

This is different from some languages where adjectives also change form.

Not exactly.

Paylaştırdı means something like:

• distributed
• portioned out
• divided up and gave/put into separate portions

In this sentence, it suggests that she took the rice pudding and split it into small bowls.

Paylaştı usually means shared.

So the difference is roughly:

• paylaştı = shared
• paylaştırdı = distributed/portioned out

Here, paylaştırdı is better because the dessert is being divided into portions.

Because herkes is grammatically treated as singular in standard Turkish.

So you say:

• Herkes beğendi. = Everyone liked it.

Not:

• Herkes beğendiler.

Even though the meaning is plural in English, the verb is singular in Turkish.

This is very common with words like:

• herkes = everyone
• kimse = no one / anyone
• biri = someone

The object is understood from context and left unstated.

Herkes çok beğendi means:

• Everyone liked it a lot.

What is it? In context, it is the rice pudding.

Turkish often omits pronouns or objects when they are obvious. So instead of repeating sütlacı, the speaker just says beğendi and lets the listener understand it.

You could make it explicit, but you usually do not need to.

The given order is natural and standard:

• Yengem = subject
• yaptığı sütlacı = object
• küçük kaselere = destination/goal
• paylaştırdı = verb
• herkes çok beğendi = second clause

Turkish is generally a verb-final language, so putting paylaştırdı and beğendi at the ends of their clauses is very normal.

Some parts can move for emphasis, for example:

• Yengem küçük kaselere yaptığı sütlacı paylaştırdı.
• Yaptığı sütlacı yengem küçük kaselere paylaştırdı.

These are possible, but the original sentence is very natural and straightforward for a learner to recognize.

Turkish often joins closely related clauses with a comma, especially in everyday written style.

So:

• Yengem yaptığı sütlacı küçük kaselere paylaştırdı, herkes çok beğendi.

means basically:

• My sister-in-law portioned the rice pudding she made into small bowls, and everyone liked it a lot.

You could also use ve in some contexts, but the comma is perfectly normal here and feels natural.