To do this, you need to be in a group that has at least the following permissions set:
Is a moderator = Yes
Can remove post = Yes
Cannot Moderate these forums: Allow all or specific forum not listed
With these set, you should see the either a link to "Open moderation options" (in forum topic list) or an "X" box to delete a specific post.
FWIW, I think some of database specific set up data scripts don't set up the Administrators group with these rights turned on. You might want to look at what rights are turned on in your Administrator group. [originally posted on jforum.net by monroe]
On re-reading your request, I think you might be asking "can you turn off anonymous postings for a forum" rather than my first impression of "delete anonymous postings".
In that case, the answer is "Yes, with some difficulty". Rights management in jForum is Group based. When you create a forum and allow anonymous postings, what happens is that all existing groups are granted that right.
To "undo" that right, you need to modify all your groups so that the Anonymous Posts are denied for the forums you don't want them in.
FWIW, a slightly less "secure" but quicker way, is to see which groups the "anonymous" user is in and just deny anonymous postings in this group. It's less "secure" because an authenticated user may be able to post anonymously. [originally posted on jforum.net by monroe]