First problem - you are being ambiguous. The subject line
says "list box" which I interpret to mean a select. Your opening
post says checkbox, which is different. You can allow the user to
select mulitple categories with either, but the details depend on
what you intend to use.
Second problem - you appear to not know much about database
design. I consider this to be the most important skill any
developer can have. If you do it well, everything else becomes
simpler. Otherwise, you are less likely to be able to translate
your data into information.