This is the 2307th most frequent Turkish word.
dengesini
"His/her/its balance."
The word 'dengesini' refers to the man's sense of balance, used possessively (his balance).
Adam dengesini kaybetti ve yere düştü.
The man lost his balance and fell to the ground.
Here 'dengesini' refers to maintaining the balance of society, implying a metaphorical balance.
Eylemlerinizle toplumun dengesini bozmayın.
Do not disturb the balance of society with your actions.
In this case, 'dengesini' is used metaphorically to denote stability in emotions or behavior.