How To Design/Link Tables - Logic Braindead

Ok, here it goes:

Got these tables:

CompanyTbl:
CompanyID (PK)
Name
Street
etc.
NAICS1(this is a standard industrial code, a 6 digit number telling about their product/service)
NAICS2
NAICS...6 (company can have 1-6 NAICS codes)

A layman has no clue what these NAICS code are, so each and one of them has a descriptive title, like NAICS 32330 = Canned Vegetables Manufacturing
For this puropse, I designed a second table:

ProductTbl
ProductTitle (PK)
NAICScode

Purpose:1. Be able to query by ProductTitle and get all companies with that profile.
2. Be able to retrieve Company ID with all its NAICS code/s and corresponding ProductTitle/s.
Now one company can have up to 6 NAICS codes and one NAICS code can appear under the descirption of multiple companies. So a many-to-many relationship. But how? A third table, probably....But how?