I use a private computer and some one is getting into my yahoo answers acct and they don't have my password How can they do that?

they can get your info if a keylogger software programmed is install in your pc a keylogger is basically software or hardware that captures keystrokes that a user enters modern one have the abilities to take screenshots etc and send the information back to the intruder. a keylogger runs in the background without you knowing personally some antivirus software will detect it and remove it if u run a full scan

they have hacked your password

They have your password. Your device is infected with malware/virus and it's sending them your account details (along with everything else you type).