Ailem, hayattaki istikrarı koruyarak mutlu yaşayabiliyor.

Ailem means my family.

It is built from:

• aile = family
• -m = my

Turkish treats aile as a singular collective noun, just like English often does with family. Even though a family contains several people, the noun itself is singular, so ailem is the normal form for my family.

Because of that, the verb is also singular here: yaşayabiliyor.

The comma is mostly a stylistic pause here. It can make Ailem feel slightly topicalized or emphasized, like:

• As for my family, ...

In everyday Turkish, the sentence can also be written without the comma:

• Ailem hayattaki istikrarı koruyarak mutlu yaşayabiliyor.

So the comma is not essential to the grammar.

Hayattaki means something like in life or the one in life / in one’s life, depending on context.

It is formed like this:

• hayat = life
• -ta / -te / -da / -de = in, at, on
• -ki = a suffix that turns that location phrase into something adjectival

So:

• hayat → hayatta = in life
• hayatta
  • -ki = hayattaki = the one that is in life / in life

In this sentence, hayattaki istikrar means the stability in life or stability in one’s life.

Because the base word is hayat, which already ends in t, and the locative suffix here is -ta.

So:

• hayat
  • -ta → hayatta

That gives two t sounds next to each other in writing. Then -ki is added:

• hayatta
  • ki → hayattaki

So the double t is completely regular.

İstikrarı has the accusative ending -ı, which marks a specific direct object.

• istikrar = stability
• istikrarı = the stability / stability as a definite object

Here, korumak means to preserve / maintain / protect, and the thing being preserved is a specific thing: the stability in life. That is why the accusative is used.

So:

• hayattaki istikrarı korumak = to preserve the stability in life

Without the accusative, the meaning would be less definite and would sound different.

Koruyarak comes from the verb korumak = to protect, preserve, maintain.

It is formed like this:

• koru- = protect/preserve
• -yarak / -erek = by doing, while doing

So koruyarak means:

• by preserving
• by maintaining
• while preserving

In this sentence, it connects the two actions:

• preserving/maintaining stability
• living happily

It can suggest both, and that is very normal in Turkish.

In this sentence, by maintaining is probably the most natural English interpretation, because it shows a means or method:

• My family can live happily by maintaining stability in life.

But while maintaining is not wrong as a literal grammatical explanation. Turkish -arak / -erek often covers both ideas: an action happening alongside another action, or an action that serves as the means to another result.

The subject is the same as the main clause subject: Ailem.

So the meaning is:

• My family, by maintaining stability in life, can live happily.

Turkish -arak / -erek forms usually share the same subject as the main verb unless context clearly shows otherwise.

In Turkish, many adjectives can also function adverbially without changing form.

So:

• mutlu = happy
• mutlu yaşamak = to live happily

English usually requires -ly in many cases, but Turkish often does not. This is very common.

So even though mutlu is basically an adjective, here it works naturally like an adverb.

Yaşayabiliyor is made of several parts:

• yaşa- = live
• -yabil- = be able to, can
• -iyor = present/imperfective marker

So:

• yaşayabiliyor = can live, is able to live, or sometimes is managing to live

The exact English translation depends on context, but the core idea is ability/possibility in the present.

Both are possible forms in Turkish, but they feel a little different.

• yaşayabilir = can live / may live / is able to live
  This is often more general or neutral.
• yaşayabiliyor = is able to live / can live
  This often feels more like a current, ongoing, real situation.

So yaşayabiliyor suggests something like:

• My family is able to live happily
• My family can manage to live happily

It can feel a bit more concrete or experiential than yaşayabilir.

The sentence follows normal Turkish patterns:

• Ailem = subject
• hayattaki istikrarı koruyarak = adverbial phrase
• mutlu = adverb-like modifier
• yaşayabiliyor = main verb

Turkish usually puts the main verb at the end, so this structure is very natural.

A rough structure is:

• Subject + modifier(s) + verb

So literally it is something like:

• My family, preserving the stability in life, happily can-live.

That sounds strange in English, but it is normal Turkish word order.

Grammatically, it is closer to the stability that is in life, because -ki creates an adjectival link.

But in natural English, you would usually translate it more simply as:

• stability in life
• stability in their life

So the Turkish form is a bit more structurally detailed than the usual English translation, but the practical meaning is the same.