If you're trying to figure out how to do date math, then this is going to seem like a very difficult task. But, in fact, what you're talking about is a perfect job for one of the Swiss Army Knives of the Unix command line: find.

Specifically, find has a flag -ctime which lets you test how long ago the file was created. The notation that the program uses for specifying dates is a bit confusing, but I'll give you a shortcut: "-ctime" lets you specify the number of days, so the command "-ctime 14" sounds right, but it actually will only match files that are exactly fourteen days old.

What we want instead, however, is "fourteen days or older", which is done by prefacing the number with a "+".

Put everything together with the peculiar syntax of find and, if you're looking for files in the directory "/var/log/test", you could use:

That'll work to identify these files, but what you're actually asking me is about directories that have this naming scheme, and it turns out that you can add another constraint to find that'll limit its results to just directories.

For this, I'm going to assume that your directories all live under the "/var/log/test" directory, but that's easily changed, of course.

To constrain results to just directories, use -type d ("-type f" is just files, for example). Put it together and:

That should identify the files you want. To automatically delete them, use "xargs" thusly:

That should do exactly what you seek!