This is the 504th most frequent Russian word.
шести
"Шести" is the genitive singular or dative singular form of "шесть" (six) or can mean "of six" / "to six" depending on context.
In this sentence, 'шести' is in the genitive case, referring to time.
Я подошёл к шести часам.
I arrived around six o'clock.
Here, 'шести' is used as the genitive form of the numeral 'шесть' when describing the castle's features.
Мы видели замок из шести башен.
We saw a castle made of six towers.
In this example, 'шести' refers to a numeric quantity (six) in a compound phrase requiring the genitive case.