Learn Turkish: Kapıyı kapatmakla güvenliği sağladı. - By closing the door, he provided security.

It combines the dictionary form (infinitive) of the verb kapatmak (to close) with the instrumental suffix -la (with/by). When you attach -la or -le (which are shortened forms of ile) to an infinitive verb, it creates an expression meaning "by doing [action]". Here, it tells us the method used to provide security.

Why does kapıyı take the accusative suffix -yı if it isn't the object of the main verb?

Even though the main verb of the sentence is sağladı (provided), the infinitive kapatmak (to close) still has verbal properties and can take its own direct object. Because "the door" is a specific, known object being closed, it gets the definite accusative suffix -yı, making it kapıyı.

What happened to the end of the word güvenlik (security) to make it güvenliği?

It takes the accusative suffix -i because it is the specific direct object of the main verb sağladı. When a vowel suffix like -i is added to a noun ending in -k, consonant mutation occurs, and the k softens into a ğ, giving us güvenliği.

Is güvenliği sağlamak a set phrase?

Yes, sağlamak means "to provide", "to supply", or "to ensure". The combination güvenliği sağlamak is a very common collocation in Turkish, used as the standard way to express "providing security" or "ensuring safety".