First, to check for understanding:
You have three tables? Supplier, Manufacturer and a Join table, supp_manu?
This would enable you to link many suppliers to a given manufacturer record and many manufacturers to a given supplier record--a classic many to many relationship.
If so, your relationships should be:
Supplier::SupplierID = Supp_Manu::SupplierID // enable the Delete and create records via this relationship options for Supp_Manu
Manufacturer::ManufacturerID = Supp_Manu::ManufacturerID // enable the Delete and create records via this relationship options for Supp_Manu
If you haven't used portals, look them up in filemaker's help for more info.
Define two value lists:
Specify Manufacturer::ManufacturerID as the first column. Manufacturer::ManufacturerName as the second column and hide the first column.
Specify Supplier::SupplierID as the first column. Supplier::SupplierName as the second column and hide the first column.
On a Supplier layout add a portal that refers to Supp_Manu.
Place the Supp_Manu::ManufacturerID field in this portal and use Field/Control | Setup... to format it as a pop up menu with Manufacturers as its value list.
Do the same on a Manufacturer layout, but use Supp_Manu::Supplier ID and the Suppliers value list.
This will only work consistantly if Supplier and Manufacturer names are unique. I'd add a validation rule to both fields to enforce that.
The pop-up menu--2 column value list with column 1 hidden is what hides the ID field values from the user.