Edit a mySQL Query that is run from a php file. Need to compare elements of comma delimited strings.

I have a SQL table that has a column called "categories" which contains a number of 15-digit alpha-numeric codes in a comma delimited string. The categories string may look something like: "9du9p08tb7oj4ic, ol888ag4nnu13q6, paidgsyegfro807." I have a php file that takes categoryIDs, which is another comma delimited string, as a parameter. Similarly, the categoryIDs string may look like: "paidgsyegfro807, f04rpd248qgmip1." I need somebody to edit the SQL line in my php file so that, amongst other criteria which do not need to be edited, the query only returns results from the table whose category string contains at least 1 similar categoryID to those passed as a parameter in the php file. I understand storing a number of strings as one comma delimited string is not good database design, but I simply do not have the time right now to redesign the database. Both a glimpse of what the database looks like and the SQL line that is ran have been uploaded with this post so that you all have an idea of what you're working with. The $sql line is the only thing that needs to be changed in this case. There is no sensitive data that is not publicly available in this database either. I am looking to pay between $30-$50 for this project as it should be a very simple fix.