Learn Turkish: Uygulamanın entegre edebileceği her şeyi programlamak mümkün. - It is possible to program everything that the application can integrate.

This is the core of the potential object relative participle taught in this lesson. It comes from entegre etmek (to integrate). First, etmek gets the ability suffix -ebil (with the t mutating to d). Then, we add the relative suffix -ecek (which softens to -eceğ). Finally, the -i is the 3rd person singular possessive suffix. The participle must have a possessive suffix that matches the subject of the relative clause.

Why is the subject written as 'uygulamanın' with the genitive suffix instead of just 'uygulama'?

In Turkish object relative clauses (translating to 'that which someone does'), the subject of the clause takes the genitive case. Here, 'the application' becomes uygulamanın. This pairs directly with the possessive suffix on the verb (edebileceği) to literally mean 'the application's integratable thing'.

Why does 'her şey' take the accusative case to become 'her şeyi'?

Because her şey (everything) is the specific direct object of the infinitive verb programlamak (to program). The relative clause just describes it, but grammatically you are programming 'everything'.

Where is the main verb of this sentence?