任何 + [noun] + 都 / 也 + [verb phrase]
没有 / 不 + [verb] + 任何 + [noun]
任何 + noun means "any" – every one of them, without exception. When the 任何 phrase comes before the verb, 都 or 也 follows it.
With a negative, 任何 is "not any, none at all". After 没有 or a negated verb, it sits in the object, and no 都 is needed.
任何时候 "any time" and 任何地方 "anywhere" work the same way, before the verb with 都.
A 任何 phrase before the verb needs 都 or 也. Without it, the sentence feels cut off.
任何 is "any at all". For "any" in an ordinary question, Chinese usually needs no word at all, or 什么.