An Archetype is the name in a card that makes it work with others.
For example, Blackwings are an archetype. Most archetype cards are stronger when working with their own archetype.
also their are archetypes that can be considered support or an archetype that shouldn't be able to make a deck, ie E Drags (last format...) and Koa'ki Meiru (These are a fun support)
Archetypes are the name that is in multiple cards and can form a specific deck. so Gorgonics, Sylvan (Shinra), Six Samurai, Blackwing, Gagaga, and i believe ZW is being called an archetype now XD.
So in the case of this homework you have been asigned you need to:
1. think of the play this archetype will work on, either spam/power/defence/or strategy.
2. the type/attribute of these monsters.
3. their effects/spells/traps.
finally 4. the archetypes name.
JD Didn't give you a lot of detail in this but that is the basic process into making an archetype.
It takes a lot of thought.... but can be really fun in the end.