This is the 4492nd most frequent Russian word.
всякой
"Всякой" means "any" or "every kind of."
Here, 'всякой' means 'all sorts of', indicating a variety of stories.
Она любит рассказывать всякой интересной истории.
She likes telling all sorts of interesting stories.
In this sentence, 'всякой' means 'any', emphasizing that this applies universally to any situation.
Во всякой ситуации надо сохранять спокойствие.
In any situation, one should maintain calmness.
The word 'всякой' here translates to 'every', suggesting a comprehensive inclusion of every individual problem.