Welcome to LQ - terse homework rules are as follows:
1. Provide what you've done so far.
1.1. Show us that you have, at least, made an attempt.
2. Don't expect us to do all of your work for you.
I'm not saying you are in conflict with point 2, it's still an item worth mentioning.
When you say "unique extension", what are you referring to? Do you mean a portion of the filename has to be unique? I ask this, simply because "extensions", while more so a leftover from the DOS world (and kept around for sake of compatibility with Windows systems), you usually do not want to use a "non-standard" file extension.
If a portion of the filename (and not the file extension) needs to be unique, then look into the date(1) command.
$ date +%m-%d-%Y