Often the topics of questions may be very private, how would a user ask a question anonymously considering their profile is linked to their other profiles on the Stack Exchange network?
If you're afraid that your account may be traced back to you in real life, you could consider making a second account:
You will want to make sure your login credentials and contact emails are completely distinct, though, so that your accounts don't get merged automatically.
Please, please make sure to register your second account as well, so you can respond to possible requests for clarifications in comments and so we can see that if you edit, it's the person that originally asked the questions that is editing it now.
If you do make a second account, make sure there's absolutely NO interaction between your two accounts:
So long as there's no voting or other dubious-looking stuff (like one account asking a question and another immediately answering it) going on between the accounts, it's really not a big deal.
This will make sure there's no way to trace back that you wrote the post, and you should be able to post very anonymously.
For this, You may create a new anonymous account which is not linked to any SE site. This way, your question can't be traced.
However, remember you shouldn't be using this account to interact with your original account in any manner.
From this meta post at Mathematics.SE,
Multiple accounts are usually tolerated, but they are not allowed to interact at all. If you are e.g. just using a different account to ask a question anonymously, this is allowed as long as you don't vote on it, don't circumvent any rate limit on it and don't interact with that account in any other way.
Interacting with your own accounts, and trying to give the impression that they belong to different users is not allowed.
From this main meta post,
It is not a problem to have multiple accounts, as long as they aren't voting for each other and doing other sockpuppet-y things.
In conclusion, you can create another account and ask a question using that without breaking any rule.