As visitors with View permissions, they would be able to see the discussion  board but not be able to reply  to any of the questions or threads there. As a site owner, you can associate permissions with permission levels and also associate permission levels with users and SharePoint groups.

By default, permissions on lists, libraries, folders, items, and documents are inherited from the parent site. However, you can break this inheritance for any securable object  at a lower level in the hierarchy by editing the permissions on that securable object (that is, creating a unique permission assignment) . For example, you can edit the permissions for a document library, which breaks the permissions inheritance from the site.

You can try to break the discussion thread’s permissions inheritance from the site, remove the unwanted permissions, then add the users who you don’t want them to reply into “SharePoint Visitors” group, then check the effect.

For more information about how to permissions and controlling access to sites, please refer to the following articles:

Permission levels and permissions
office.microsoft.com/.../HA101001491033.aspx

About controlling access to sites and site content
office.microsoft.com/.../HA101001441033.aspx