Freedom was challenged with/by the clashing wills of powerful states and evil designs of tyrants.
Which one to use "by" or "with"?
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For this example, you should use "by". "Freedom was challenged by the clashing wills..."
"to challenge with" is a transitive verb that requires some object that acts usually appears as an -ing gerund phrase. You'd see that usage in sentences like "The representative was challenged with fixing the problematic issue." or "Arlene was challenged with fixing the clogged drain that she knew nothing about how to fix."
The difference may be subtle, but if you use "challenge by", then you need some object that can literally "do" a challenge (often animate)—whereas "challenge with" is an inanimate issue that itself "is" a challenge to be overcome.