Yeni kitabımı arkadaşıma göstermeden edemiyorum.

A helpful breakdown is:

• yeni = new
• kitabımı = my book
  • the direct-object ending
• arkadaşıma = to my friend
• göstermeden = without showing
• edemiyorum = I cannot do

So the structure is roughly:

• Yeni kitabımı = my new book
• arkadaşıma = to my friend
• göstermeden edemiyorum = I can’t help showing / I can’t refrain from showing

A more literal version would be something like:

I cannot manage not to show my new book to my friend.

Because kitap changes to kitab- before a vowel-initial suffix. This is a very common sound change in Turkish called consonant softening.

• kitap = book
• kitabım = my book
• kitabımı = my book (as the direct object)

What is happening:

• final p often becomes b
• when a suffix beginning with a vowel is added

So:

• kitap + ım → kitabım
• kitabım + ı → kitabımı

That -ı is the accusative case ending, which marks a specific direct object.

Here, the thing being shown is the speaker’s specific new book, so Turkish marks it.

• kitabım = my book
• kitabımı = my book as the object of the verb

With göstermek (to show), you usually have:

• the thing shown = direct object
• the person you show it to = dative

So in this sentence:

• kitabımı = the thing being shown
• arkadaşıma = the person it is shown to

Because göstermek takes the person receiving the thing in the dative case, not the accusative.

Compare:

• Bir şeyi gösteriyorum. = I am showing something.
• Birine gösteriyorum. = I am showing it to someone.

So:

• kitabımı = my book (what I show)
• arkadaşıma = to my friend (to whom I show it)

If you said arkadaşımı, that would make my friend the direct object, which would not fit this meaning.

It comes from:

• arkadaş = friend
• arkadaşım = my friend
• arkadaşıma = to my friend

So the parts are:

• arkadaş
  • -ım = arkadaşım
• arkadaşım
  • -a = arkadaşıma

The -a is the dative ending, meaning to.

The ending -meden / -madan usually means without doing.

So:

• göstermek = to show
• göstermeden = without showing

This form connects one action to another. On its own, it often has a very literal meaning:

• Gitmeden ara. = Call before leaving / Don’t leave without calling.
• Yemeden çıktım. = I left without eating.

In your sentence, though, it is part of a very common pattern:

• -meden edememek

That pattern has a more idiomatic meaning.

Because -meden edememek is a set expression in Turkish.

The pattern:

• X-meden edememek

means:

• cannot help doing X
• cannot refrain from doing X
• cannot resist doing X

So:

• göstermeden edemiyorum literally looks like I cannot do without showing
• but idiomatically it means I can’t help showing

This is one of those constructions where the whole pattern matters more than the literal word-for-word translation.

Other examples:

• Gülmeden edemiyorum. = I can’t help laughing.
• Sormadan edemedi. = He/She couldn’t help asking.
• Bakmadan edemem. = I can’t resist looking.

Because gösteremiyorum means something very different.

• gösteremiyorum = I cannot show
• göstermeden edemiyorum = I cannot help showing

These are almost opposites in practice:

• gösteremiyorum suggests lack of ability, chance, permission, or possibility
• göstermeden edemiyorum suggests an urge or inability to resist

So if you say:

• Yeni kitabımı arkadaşıma gösteremiyorum.

  that would mean something like:

• I can’t show my new book to my friend.

But the original sentence means:

• I end up showing it because I can’t help myself.

It comes from etmek (to do), but in this expression it is part of the fixed pattern -meden edememek.

Roughly:

• etmek = to do
• edemiyorum = I cannot do

The form changes from et- to ed- here, which is normal for this verb in many forms:

• etmek
• ediyor
• edemiyorum

So göstermeden edemiyorum is not really about doing in a literal sense. It is the standard grammatical way of saying I can’t help showing.

It is in the present continuous form:

• -iyor

So:

• edemiyorum = I am not able to / I can’t

In Turkish, the present continuous is used very often, not only for actions happening right now, but also for:

• current situations
• repeated behavior
• emotional tendencies
• things that are true these days

So here it can mean something like:

• Right now, I can’t help showing it
• These days, I just can’t resist showing it

Because Turkish usually does not need subject pronouns when the verb already shows the person.

In edemiyorum, the ending -um tells you the subject is I.

So:

• edemiyorum = I can’t
• edemiyorsun = you can’t
• edemiyor = he/she/it can’t

You could add ben for emphasis:

• Ben yeni kitabımı arkadaşıma göstermeden edemiyorum.

But normally it is unnecessary.

Because Turkish adjectives do not agree with nouns the way they do in some other languages.

So:

• yeni kitap = new book
• yeni kitabım = my new book
• yeni kitabımı = my new book (object)

The adjective yeni stays the same. The endings go on the noun, not on the adjective.

The most neutral order puts the main verb at the end, which is exactly what we have here.

• Yeni kitabımı arkadaşıma göstermeden edemiyorum.

This is very natural Turkish.

Turkish word order is somewhat flexible, though. You can move parts around for emphasis, especially before the final verb. For example, you might emphasize arkadaşıma or yeni kitabımı by placing it earlier or closer to the verb.

But the final verb position is still the most important basic rule, and the original sentence sounds fully natural.

Yes. -meden edememek is a very common and natural pattern.

It is especially used when someone:

• cannot resist doing something
• does something almost automatically
• feels an impulse they cannot control

So this sentence sounds natural and idiomatic, not artificial or overly literal.

It has the flavor of:

• I just can’t help showing my new book to my friend.
• I can’t resist showing my new book to my friend.