This is the 14407th most frequent German word.
kasachischen
"Kasachischen" means "Kazakh" (adjective, relating to Kazakhstan or its people).
The word 'kasachischen' is used as an adjective here to describe 'Hauptstadt' (capital), specifying that the capital is Kazakh.
Ich habe einen Freund aus der kasachischen Hauptstadt Astana.
I have a friend from the Kazakh capital Astana.
In this sentence, 'kasachischen' serves as an adjective describing 'Traditionen' (traditions), indicating that the traditions pertain to Kazakhstan.
Die kasachischen Traditionen sind sehr reichhaltig und vielfältig.
The Kazakh traditions are very rich and diverse.
Here, 'kasachischen' modifies 'Schachmeisterschaften' (chess championships), showing they are related to Kazakhstan.