Kuzenim sahilde yürürken beyaz şort giymeyi seviyor.

Kuzenim means my cousin.

It is built like this:

• kuzen = cousin
• -im = my

So Turkish often says possession by adding a suffix directly to the noun, instead of using a separate word like my.

Examples:

• arkadaşım = my friend
• evim = my house
• kuzenim = my cousin

Because -de is the locative ending, which means in / on / at a place.

• sahil = beach / shore
• sahilde = on the beach / at the beach

So sahilde yürürken means while walking on the beach.

A few similar examples:

• evde = at home
• okulda = at school
• parkta = in the park

Yürürken means while walking.

It comes from:

• yürümek = to walk
• yürür = walks / is in the habit of walking / walking-form used here
• -ken = while

So:

• yürürken = while walking

This -ken structure is very common in Turkish:

• yemek yerken = while eating
• konuşurken = while speaking
• okurken = while reading

In this sentence, it gives background action: while on the beach walking...

Both can exist, but yürürken is the more common and natural form here.

Turkish often uses:

• verb stem + -(A)r + ken for while doing
• so yürürken = while walking

You may also hear forms based on other tense/aspect shapes in some contexts, but for a learner, yürürken is the standard and most useful pattern to remember.

So:

• gelirken = while coming
• giderken = while going
• yürürken = while walking

Here beyaz şort is just the noun phrase white shorts.

• beyaz = white
• şort = shorts

Turkish adjectives do not change for number or gender, and they come before the noun:

• beyaz şort = white shorts
• büyük ev = big house
• uzun yol = long road

Also, şort is often used in Turkish as a singular-looking noun even when English uses shorts. So şort giymek naturally means to wear shorts.

Because sevmek here takes a verbal noun as its object.

• giymek = to wear
• giymeyi = wearing / to wear, as the object of another verb

Structure:

• giymeyi seviyor = likes wearing / likes to wear

This is a very common Turkish pattern:

• yüzmeyi seviyorum = I like swimming
• kitap okumayı seviyor = he/she likes reading books
• kahve içmeyi seviyoruz = we like drinking coffee

So the -yI ending here marks the verbal noun as the object of seviyor.

The -y- is a buffer consonant.

Without case:

• giyme = wearing

When the accusative ending is added:

• giyme + i would be awkward
• so Turkish inserts y
• giymeyi

This happens often when one vowel-ending form meets another vowel-beginning ending.

Compare:

• okuma → okumayı
• yazma → yazmayı
• giyme → giymeyi

Both relate to liking, but seviyor is the natural choice here.

• seviyor = likes / is fond of
• sever can also mean likes, but often sounds more general, habitual, or slightly more formal depending on context

In everyday Turkish, X yapmayı seviyor is a very common way to say he/she likes doing X.

So:

• beyaz şort giymeyi seviyor = he/she likes wearing white shorts

This is one of those places where Turkish often prefers the present continuous form for a general personal preference.

The sentence is:

• Kuzenim = my cousin
• sahilde yürürken = while walking on the beach
• beyaz şort giymeyi = wearing white shorts
• seviyor = likes

So the structure is roughly:

[Subject] + [time/circumstance phrase] + [object] + [verb]

This is very normal Turkish word order, since Turkish usually places the main verb at the end.

A rough word-for-word order is: My cousin [on the beach while walking] [wearing white shorts] likes.

In natural English, the meaning is:

My cousin likes wearing white shorts while walking on the beach.

So sahilde yürürken most naturally gives the situation for wearing the white shorts.

It does not usually mean:

• My cousin, who is walking on the beach, likes white shorts in general

Instead, it suggests:

• during beach walks, my cousin likes to wear white shorts

Turkish often leaves this kind of attachment slightly flexible, but in normal interpretation, it connects with the whole activity beyaz şort giymek.

Because Turkish often expresses meanings like while, when, or during with suffixes instead of separate words.

Here, -ken does the job of while:

• yürürken = while walking

So instead of saying something like while he/she walks, Turkish compresses that idea into one word.

This is very common in Turkish grammar:

• gelince = when he/she comes
• gülerken = while laughing
• çalışırken = while working

Yes. Turkish uses şort as the normal noun, and it does not have to match English singular/plural habits.

So:

• şort can correspond to English shorts
• bir şort = a pair/item of shorts
• şortlar = shorts, if you explicitly mean multiple pairs

In this sentence, beyaz şort giymek is the natural way to say to wear white shorts.

Yes, there are other possible ways, but this sentence is already natural.

Some alternatives might be:

• Kuzenim sahilde yürürken beyaz şort giymeyi çok seviyor.
  = My cousin really likes wearing white shorts while walking on the beach.

• Kuzenim sahilde yürüyüş yaparken beyaz şort giymeyi seviyor.
  = My cousin likes wearing white shorts while taking a walk on the beach.

• Kuzenim sahilde yürürken beyaz şort giymekten hoşlanıyor.
  = My cousin enjoys wearing white shorts while walking on the beach.

The original sentence is a good everyday example of:

• possession suffixes
• locative case
• -ken
• verbal noun + accusative
• verb-final word order