Different Parent Content Types like Item, Announcement, Issue, Contact are not avaliable under List Content Types
While Creating New Content Types in Site Settings, above content types are not appearing in Parent Content Types Dropdown.
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Your question is pretty vague, so I can only give some basic instruction.
First of all, try and see if the content type you are searching is under another category from the "Select parent content type from" dropdown. I think this is pretty obvious, but it is still worth to check.
Second, know that some of the available content type are provisoned by feature normally not activated by default on most site collection / web site template. If I recall correctly, the Issue content type is dependent on an hidden feature called
IssuesList, while the Announcement one is dependent on the
AnnouncementsList hidden feature. Both should be included when you activate the visible
Team Collaboration Lists feature.
I suggest that you check if you can create lists of the Announcement template. If that one is missing too, check the feature you have activated in your environment - probably you are just missing an activation somewhere.