When I go to accknowledge it, it shows accknowledged by SYSMAN. It does not allow me to me accknowledge.
Which table I need to clean so that it does not show the old alerts in OEM...?
I wouldn't do that.
"Oracle clears most of the alerts automatically after the cause of the alert disappears. Some alerts need to be acknowledged by the DBA, while others may require corrective measures. After you take necessary corrective actions, acknowledge the alert by clearing it or purging it. The cleared alert is sent to the Alert History, which is viewable from the OEM home page under Related Links; purged alerts are deleted from the Alert History.
From the Home page, click on the Alerts link and select the alert to be cleared from the Alerts page. Choose Clear or Purge to act on the alert. You can also choose the Clear Every Open Alert or Purge Every Alert option from this screen, but neither one is a good choice."
Disclaimer: Advice is provided to the best of my knowledge but no implicit or explicit warranties are provided. Since the advisor explicitly encourages testing any and all suggestions on a test non-production environment advisor should not held liable or responsible for any actions taken based on the given advice.