Bu etek sana çok yakışıyor.

Because yakışmak normally takes the person in the dative case: to someone.

• sen = you
• sana = to you

So Bu etek sana çok yakışıyor is literally something like:

• This skirt suits to you very much

That sounds unnatural in English, but the grammar idea is important: with yakışmak, Turkish marks the person with the dative.

Examples:

• Bu renk bana yakışıyor. = This color suits me.
• Mavi sana yakışıyor. = Blue suits you.

Yakışıyor comes from the verb yakışmak, which means:

• to suit
• to look good on
• to be becoming

So in this sentence, it means the skirt looks good on the person being addressed.

A useful point: yakışmak is not just about being beautiful in general. It means something is a good match for someone.

For example:

• Elbise güzel. = The dress is beautiful.
• Elbise sana yakışıyor. = The dress suits you.

Those are related, but not the same idea.

Yakışıyor is the -iyor form, often called the present continuous. But in Turkish, this form is also very commonly used for things that English would express with the simple present.

So:

• Bu etek sana çok yakışıyor.

can mean:

• This skirt suits you very well.
• This skirt is looking really good on you.

It does not always have to mean something temporary happening right this second. In everyday Turkish, -iyor is often the natural choice for comments like this.

Because çok is functioning as an adverb here, meaning very or really, and it modifies the verb phrase.

So:

• çok yakışıyor = suits very well / really suits

This is very normal Turkish word order. Adverbs often come before the word or phrase they modify.

Compare:

• Bu sana yakışıyor. = This suits you.
• Bu sana çok yakışıyor. = This suits you a lot / very well.

Because etek is the subject here, and subjects are normally in the nominative, which usually has no ending.

• etek = skirt
• bu etek = this skirt

There is no accusative ending because the skirt is not the direct object here. It is the thing that does the suiting, grammatically speaking.

Structure:

• Bu etek = subject
• sana = to you
• çok yakışıyor = suits very well

The given order is very natural, but Turkish word order is flexible.

Default, neutral order here is:

• Bu etek sana çok yakışıyor.

But you could also say:

• Sana bu etek çok yakışıyor.
• Bu etek çok yakışıyor sana.
  (more marked, often more conversational or emphatic)

The verb usually comes at the end in standard Turkish, but other parts can move around for emphasis or style.

For example:

• Sana first can emphasize you
• Bu etek first feels like the neutral topic: this skirt

Here bu means this.

• bu etek = this skirt

Turkish does not have articles like the and a/an in the same way English does. So bu is specifically a demonstrative, not an article.

Compare:

• etek = skirt / the skirt / a skirt, depending on context
• bu etek = this skirt
• şu etek = that skirt / that skirt there
• o etek = that skirt

No. It is often used for clothes, but also for many other things that suit a person.

Examples:

• Bu renk sana yakışıyor. = This color suits you.
• Kısa saç sana yakışıyor. = Short hair suits you.
• Bu gözlükler sana yakışıyor. = These glasses suit you.
• Ciddiyet ona yakışıyor. = Seriousness suits him/her.

So the general idea is: something fits someone well in appearance, style, or even manner.

Negative:

• Bu etek sana yakışmıyor. = This skirt doesn’t suit you.

Question:

• Bu etek sana yakışıyor mu? = Does this skirt suit you?

Negative question:

• Bu etek sana yakışmıyor mu? = Doesn’t this skirt suit you?

Notice that mu is the question particle, and it is written separately.

Yes. Yakışıyor simply means it suits you, while çok yakışıyor means it suits you very much / it looks really good on you.

Compare:

• Bu etek sana yakışıyor. = This skirt suits you.
• Bu etek sana çok yakışıyor. = This skirt suits you really well.

In conversation, çok often sounds warmer and more complimentary.

It comes from:

• yakış- = verb stem
• -ıyor = present continuous suffix

So:

• yakışıyor = it is suiting / it suits

The vowel in -ıyor follows vowel harmony. Since the last vowel in yakış is ı, the suffix appears as -ıyor.

Other possible forms of this suffix are:

• -iyor
• -ıyor
• -uyor
• -üyor

depending on the verb.

You can, but it will sound unnatural in English.

Word-by-word:

• Bu = this
• etek = skirt
• sana = to you
• çok = very / much
• yakışıyor = suits / looks good on

A very literal gloss would be:

• This skirt suits you very much.

Natural English would usually be:

• This skirt suits you very well.
• This skirt looks really good on you.

So the literal breakdown is useful for grammar, but not always for natural translation.