If your
public_html/ directory is password protected, that password will apply to your entire site. Do you want to have the password apply only to part of the site? If so, you will need to remove the password protection from
public_html/ (or "/") and create it for "deeper" directories, such as
public_html/jpegs/ (or "/jpegs").
While
stockthestore.com and
www.stockthestore.com are just different names for the same site (your
public_html/ or "/" directory), as far as I know, the password protection considers them to be different (you get passwords stored in different session cookies for the two names). If you have a
public_html/index.html that points to the jpegs directory, you can just edit that file to
...href="http://www.stockthestore.com/jpegs... or even just
...href="/jpegs.... Feel free to edit any index.htm or index.html file -- you can use cPanel > File Manager, navigate to the directory the file is in, click on the file name, click on "edit the file" (on the right side of the screen). Just edit index.* files until you end up with consistent site names (all with or all without "www."). You don't need the site name if you're pointing to a directory and file on the same site -- just give
/jpegs/index.htm or whatever.