Normally, it is not possible to change your Battle.net account security question and answer once you have set it. However, as happened during the 2012 security breach, special circumstances let you reset this information. If your account was compromised, you'll need to contact Blizzard with identifying information to prove ownership of the account. Without this information, you won't be able to change the security question.
Contacting Blizzard Support
Calling Blizzard's phone support gives you the opportunity to reset your security information as long as you can prove your identity. Make sure you know the account name, billing address and product key from a game registered to the account. For instance, if you have a copy of "World of Warcraft" added on your Battle.net account, providing the product key from the box is a surefire way to prove your ownership.
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