This is the 11094th most frequent Turkish word.
dumanından
"From its smoke."
In this case, 'dumanından' is used to describe 'from the steam' of the tea, implying observation of a sign.
Çayın dumanından sıcak olduğunu anladık.
We understood from the tea's steam that it was hot.
In this sentence, 'dumanından' refers to 'from the smoke' belonging to the mountain, indicating its source.
Dağın dumanından etkilenen köylüler evlerine döndüler.
The villagers, affected by the mountain's smoke, returned to their homes.
Here, 'dumanından' indicates 'from the smoke' caused by the fire, specifying the origin of the difficulty.