I actually started putting an answer together, but I ran into complications, because you (quite understandably) want a simple example. The problem is manifold.
First I don't have a good idea of your level of actual expertise re Relational Databases and 5NF; I don't have a starting point to take up and then discuss the specifics of 6NF,
Second, just like any of the other NFs, it is variegated. You can just barely step into it; you can implement 6NF for certan tables; you can go the full hog on every table, etc. Sure there is an explosion of tables, but then you Normalise that, and kill the explosion; that's an advanced or mature implementation of 6NF. No use providing the full or partial levels of 6NF, when you are asking for the simplest, most straight-forward example.
I trust you understand that some tables can be "in 5NF" while others are "in 6NF".
So I put one together for you. But even that needs explanation.
Now SQL barely supports 5NF, it does not support 6NF at all (I think dportas says the same thing in different words). Now I implement 6NF at a deep level, for performance reasons, simplified pivoting (of entire tables; any and all columns, not the silly PIVOT function in MS), columnar access, etc. For that you need a full catalogue, which is an extension to the SQL catalogue, to support the 6NF that SQL does not support, and maintain data Integrity and business Rules. So, you really do not want to implement 6NF for fun, you only do that if you have a need, because you have to implement a catalogue. (This is what the EAV crowd do not do, and this is why most EAV systems have data integrity problems. Most of them do not use the declarative Referential & Data Integrity that SQL does have.)
But most people who implement 6NF don't implement the deeper level, with a full catalogue. They have simpler needs, and thus implement a shallower level of 6NF. So, let's take that, to provide a simple example for you. Let's start with an ordinary Product table that is declared to be in 5NF (and let's not argue about what 5NF is). The company sells various different kinds of Products, half the columns are mandatory, and the other half are optional, meaning that, depending on the Product Type, certain columns may be Null. While they may have done a good job with the database, the Nulls are now a big problem: columns that should be Not Null for certain ProductTypes are Null, because the declaration states NULL, and their app code is only as good as the next guy's.
So they decide to go with 6NF to fix that problem, because the subtitle of 6NF states that it eliminates The Null Problem. Sixth Normal Form is the irreducible Normal Form, there will be no further NFs after this, because the data cannot be Normalised further. The rows have been Normalised to the utmost degree. The definition of 6NF is:
a table is in 6NF when the row contains the Primary Key, and at most one, attribute.
Notice that by that definition, millions of tables across the planet are already in 6NF, without having had that intent. Eg. typical Reference or Look-up tables, with just a PK and Description.
Right. Well, our friends look at their Product table, which has eight non-key attributes, so if they make the Product table 6NF, they will have eight sub-Product tables. Then there is the issue that some columns are Foreign Keys to other tables, and that leads to more complications. And they note the fact that SQL does not support what they are doing, and they have to build a small catalogue. Eight tables are correct, but not sensible. Their purpose was to get rid of Nulls, not to write a little subsytem around each table.
Simple 6NF Example
Readers who are unfamiliar with the Standard for Modelling Relational Databases may find IDEF1X Notation useful in order to interpret the symbols in the example.
So typically, the Product Table retains all the Mandatory columns, especially the FKs, and each Optional column, each Nullable column, is placed in a separate sub-Product table. That is the simplest form I have seen. Five tables instead of eight. In the Model, the four sub-Product tables are "in 6NF"; the main Product table is "in 5NF".
Now we really do not need every code segment that SELECTs from Product to have to figure out what columns it should construct, based on the ProductType, etc, so we supply a View, which essentially provides the 5NF "view" of the Product table cluster.
The next thing we need is the basic rudiments of an extension to the SQL catalog, so that we can ensure that the rules (data integrity) for the various ProductTypes are maintained in one place, in the database, and not dependent on app code. The simplest catalogue you can get away with. That is driven off ProductType, so ProductType now forms part of that Metadata. You can implement that simple structure without a catalogue, but I would not recommend it.
Update
It is important to note that I implement all Business Rules in the database. Otherwise it is not a database (the notion of implementing rules "in application code" is hilarious in the extreme, especially nowadays, when we have florists working as "developers"). Therefore all rules, etc are first and foremost implemented as SQL declarations, CHECK constraints, functions, etc. That preserves all Declarative Referential Integrity, and declarative Data Integrity. The extension to the SQL catalog covers the area that SQL does not have declarations for, and they are then implemented as SQL. Being a good data dictionary, it does much more. Eg. I do not write Views every time I change the tables or add or change columns or their characteristics, they are created directly from the catalog+extension using a simple code generator.
One more very important note. You cannot implement 6NF (or EAV properly, for that matter), without completing a full and faithful Normalisation exercise, to 5NF. The problem I see at every site is, they don't have a genuine 5NF state, they have a mish-mash of partial normalisation or no normalisation at all, but they are very attached to that. Creating either 6NF or EAV from that is a disaster. Creating EAV or 6NF from that without all business rules implemented in declarative SQL is a nuclear disaster, burning for years. You get what you pay for.
End update.
Finally, yes, there are at least four further levels of Normalisation (Normalisation is a Principle, not a mere reference to a Normal Form), that can be applied to that simple 6NF Product cluster, providing more control, less tables, etc. The deeper we go, the more extensive the catalogue. And higher levels of performance. When you are ready, just ask, I have already erected the models and posted details in other answers.
