Here is the solution provided by Yahoo Customer Care:
Go to this page
Select password and sign in
Select forgot password
Click on "password helper" or
Click on the phone to get the Yahoo customer service phone number for your region. (Canada or USA) (You may have to wait a very long time before a customer care assistant answers you)
click on the envelope to open an e-mail case. If you do not know your security question, in the space provided for them, write "unknown"