This is the 3068th most frequent Turkish word.
başındaki
"Başındaki" means "the one on your head" or "on the head."
Here, "başındaki" means 'on your head,' indicating a possessive and locative description.
Başındaki şapka çok güzel.
The hat on your head is very beautiful.
In this sentence, "başındaki" is used figuratively to mean 'that you are leading,' referring to the project.
Başındaki proje hakkında konuşmaya ne dersin?
What do you think about talking about the project you are leading?
Here, "başındaki" refers to 'that you are facing,' indicating a person metaphorically dealing with issues.