İndirim kuponunu kasada göstereceğim.

Because indirim kuponu is a noun compound in Turkish.

• indirim = discount
• kuponu = coupon, but here the -u is part of the compound structure

In Turkish, combinations like discount coupon, car door, school bus are often made with a special pattern where the second noun takes a suffix. So:

• indirim kuponu = discount coupon

Then, because this noun phrase is the definite direct object of the sentence, it also takes the accusative ending. After that compound suffix, Turkish uses a buffer n:

• indirim kuponu
  • accusative → indirim kuponunu

So the full form is correct and very natural.

It is a very common Turkish structure called an indefinite noun compound.

Pattern:

• first noun: describes the type
• second noun: gets a suffix

So:

• indirim kuponu = discount coupon
• literally, something like coupon of discount, though in natural English we just say discount coupon

Other examples:

• otobüs durağı = bus stop
• telefon numarası = phone number
• kahve fincanı = coffee cup

This is one of the most important noun patterns in Turkish.

The ending -da here is the locative case, which often means in, on, or at, depending on context.

• kasa = cash register / checkout / till
• kasada = at the register / at the checkout

So kasada does not necessarily mean physically inside the cash register. In this context, it naturally means at the checkout or at the register.

This ending changes by vowel harmony and consonant harmony:

• evde = at home
• okulda = at school
• masada = on the table
• kasada = at the register

It breaks down like this:

• göster- = show
• -ecek = future tense suffix
• -im = I

So the basic pieces are:

• göster + ecek + im

In actual spelling and pronunciation, this becomes:

• göstereceğim = I will show

A useful thing to notice:

• the future tense is -ecek or -acak
• which one appears depends on vowel harmony

Examples:

• gideceğim = I will go
• yapacağım = I will do
• göstereceğim = I will show

Also, the k in -ecek often softens to ğ before a vowel-initial personal ending:

• -ecek + im → -eceğim

Turkish often omits the subject pronoun when it is already clear from the verb ending.

Here, -ceğim already tells you the subject is I.

So:

• göstereceğim = I will show

Because of that, ben is unnecessary unless you want emphasis.

Compare:

• İndirim kuponunu kasada göstereceğim. = I will show the discount coupon at the register.
• Ben indirim kuponunu kasada göstereceğim. = I will show the discount coupon at the register.
  (This sounds more emphatic.)

Yes. The most neutral Turkish word order is often:

• Subject – Object – Verb

So this sentence follows a very normal pattern:

• İndirim kuponunu = object
• kasada = place
• göstereceğim = verb

Turkish is more flexible than English, though. You can move parts around for emphasis or focus.

For example:

• Kasada indirim kuponunu göstereceğim.
• İndirim kuponunu göstereceğim kasada.
  This is possible in some contexts, but less neutral.

The version you were given sounds standard and natural.

Turkish does not have articles like English a and the in the same way.

Instead, definiteness is often shown by grammar, especially with direct objects.

Here, the object has the accusative marking:

• indirim kuponunu

That marking strongly suggests a specific, known coupon, so in English it is usually translated with the:

• the discount coupon

Compare:

• İndirim kuponu göstereceğim. = I will show a discount coupon / discount coupon(s), depending on context
• İndirim kuponunu göstereceğim. = I will show the discount coupon

So in many cases, the accusative ending works a bit like a signal of definiteness.

Not exactly.

• kasada = at the register / at the checkout
• kasiyere = to the cashier

So:

• İndirim kuponunu kasada göstereceğim.
  = I’ll show the discount coupon at the register

• İndirim kuponunu kasiyere göstereceğim.
  = I’ll show the discount coupon to the cashier

Both are natural, but they focus on slightly different things:

• kasada focuses on the place
• kasiyere focuses on the person receiving the action

A rough syllable breakdown is:

• İn-di-rim
• ku-po-nu-nu
• ka-sa-da
• gös-te-re-ce-ğim

A few important pronunciation notes:

• İ = like i in machine, but shorter
• ı = a sound English does not really have; keep it short and unrounded
• ö = similar to German ö or French eu
• c in Turkish = j as in jam
• ğ usually softens or lengthens the previous vowel rather than sounding like a strong consonant

So göstereceğim is approximately:

• gös-te-re-jee-im,
  though that is only a rough English-style guide

Try saying it smoothly:

• İndirim kuponunu kasada göstereceğim.

Yes, but the meaning changes.

• İndirim kuponunu göstereceğim
  = I will show the discount coupon
  → a specific coupon

• İndirim kuponu göstereceğim
  = I will show a discount coupon / discount coupon(s)
  → less specific

This is a very important Turkish contrast:

• accusative object = usually definite/specific
• bare object = often indefinite or non-specific

So the ending is not just decoration; it changes how specific the object sounds.