This is the 10592nd most frequent Turkish word.
bırakmayacağının
"Of not letting go" or "that you will not leave."
The word 'bırakmayacağının' here is used to convey the notion that the subject will not abandon their friend, forming a future negative commitment.
Söz verdi ki, arkadaşını tehlikede bırakmayacağının garantisi vardı.
He promised that there was a guarantee he would not leave his friend in danger.
In this sentence, 'bırakmayacağının' refers to the assurance that the project will not be abandoned halfway.
Projeyi yarıda bırakmayacağının sözü verildi.
The promise was made that the project would not be left incomplete.
Here, 'bırakmayacağının' highlights the understanding that the person addressed will ensure the plants are regularly watered and not neglected.