Bu koyu renkli ceket çok beğeniliyor.

• Bu = this
• koyu renkli = dark-colored
• ceket = jacket
• çok = a lot / very much
• beğeniliyor = is liked / is being liked

A very literal translation is:

This dark-colored jacket is liked a lot.

In more natural English, it can also mean something like:

This dark-colored jacket is very popular.

koyu renkli means dark-colored.

It is made of:

• koyu = dark
• renk = color
• -li = a suffix meaning with / having

So:

• renkli = colored / having color
• koyu renkli = dark-colored

This -li suffix is very common in Turkish:

• şekerli = with sugar / sugary
• tuzlu = salty / with salt
• uzun saçlı = long-haired

Because ceket is the subject of the sentence, and subjects in Turkish are normally in the basic form, with no case ending.

Here, the sentence is passive:

• Bu koyu renkli ceket çok beğeniliyor.
• This dark-colored jacket is liked a lot.

If you made it active, ceket would become the object and would usually take the accusative ending:

• Herkes bu koyu renkli ceketi çok beğeniyor.
• Everyone likes this dark-colored jacket a lot.

So:

• ceket = subject
• ceketi = object

beğeniliyor comes from the verb beğenmek, which means to like, to admire, or to find appealing.

It breaks down like this:

• beğen- = verb stem, like / admire
• -il- = passive suffix, be liked
• -iyor = present continuous / present-time marker

So beğeniliyor means:

is being liked
or more naturally here, is liked

There is no extra ending after that because the subject is third person singular: ceket.

Turkish often uses the passive when the focus is on the thing people like, not on who likes it.

So:

• Bu koyu renkli ceket çok beğeniliyor. = This dark-colored jacket is liked a lot.

Instead of:

• İnsanlar bu koyu renkli ceketi çok beğeniyor. = People like this dark-colored jacket a lot.

The passive sounds natural when talking about clothes, products, designs, songs, films, and similar things. In English, we often translate this kind of Turkish passive more naturally as is popular or is well liked.

Not necessarily.

The -(i)yor form is often taught as the present continuous (is doing), but in real Turkish it can also describe:

• something happening now
• a general present situation
• a repeated or ongoing state

So here, beğeniliyor does not have to mean people are liking the jacket at this exact second. It can mean more generally:

This jacket is well liked.
This jacket is popular.

Here, çok means a lot / very much, because it is modifying the verb.

• çok beğeniliyor = is liked a lot

Compare:

• çok güzel = very beautiful
  here çok modifies an adjective
• çok seviyor = likes/loves very much
  here çok modifies a verb

So in this sentence, çok is closer to very much than to very.

Not in this sentence, unless you change the structure.

• beğeniliyor = is liked
• beğeniyor = likes

So:

• Bu koyu renkli ceket çok beğeniliyor. = This dark-colored jacket is liked a lot.

But if you say:

• Bu koyu renkli ceket çok beğeniyor that would literally mean:
• This dark-colored jacket likes ... a lot which does not make sense, because the jacket would become the one doing the liking.

To use beğeniyor, you need a real subject:

• Ayşe bu koyu renkli ceketi çok beğeniyor.
• Ayşe likes this dark-colored jacket a lot.

To some extent, yes. Turkish word order is flexible, but the neutral order here is:

Bu koyu renkli ceket çok beğeniliyor.

The noun phrase bu koyu renkli ceket should stay together:

• bu = this
• koyu renkli = dark-colored
• ceket = jacket

You can move other parts for emphasis, especially in speech or writing, for example:

• Bu koyu renkli ceket beğeniliyor.
• Çok beğeniliyor bu koyu renkli ceket.
  This is more marked and emphasizes çok beğeniliyor.

For learners, the safest version is the original one.

Because beğenmek is usually the more natural verb for things like clothes, styles, designs, or products.

• beğenmek = to like / admire / find attractive / approve of
• sevmek = to love / like in a broader, often more personal sense

For a jacket, beğenmek is the normal choice:

• Bu ceketi beğendim. = I liked this jacket.

Using sevmek for objects is possible in some contexts, but beğenmek is more standard when you mean that something looks good or appeals to people.

The ğ in Turkish is usually not pronounced like a hard English g.

In beğeniliyor, it is roughly pronounced like:

be-eniliyor

So the full sentence is approximately:

boo koyu renkli jeket chok be-eniliyor

A few useful pronunciation points:

• bu sounds like boo
• ceket starts with c = j as in jam
• çok has ç = ch
• ğ usually softens or lengthens the sound rather than being pronounced as a strong consonant

So do not pronounce beğeniliyor like beg-eniliyor with a hard g.