Hi, is there a way I can restrict new users from posting in certain topics or forums until they have a certain number of posts under their profile? For example, a new user needs to have 20 posts in all the other forums before they can post in one specified forum.

Yes, you need to make a new group. And edit permissions for the group.
Control Panel » Group Management
You will see a post count field to the right of users.
Whatever number you enter the member will be promoted to that group after the posts exceed that number.
Select the New group tab on the bottom left.
Add a new group.
Go back to:
Control Panel » Group Management
Set permissions for the group using the links on the right forums,site,cp

Then goto:
Control Panel » Registration Settings
Set the
Default Group(s) for New Members: to the newbie group you created.
I think that is it.
So a new registration will become a member of the newbie group.
With the permissions you set for newbies.
They will be promoted to users after the number of posts you set.

Thanks Ruben! Ive tried to figure it out but didn't think of using the group function.

Yea, You could do it several different ways with the groups.
it is a little bit more involved with a existing board.

But even if you set the user group to say a 100 they should not be demoted back to the newbie group.
You would need to do that through cp>> member management