Archaebacterias and eubacterias both come under Kingdom Monera.
Archaebacterias can survive in harsh habitats like in extreme salty areas (halophiles), hot springs (thermoacidophils) and marshy areas (methanogens). They can survive in such harsh conditions because they have a different kind of cell wall.
Eubacterias are the true bacterias. They can be identified by the presence of a rigid cell wall. Also, if they happen to be motile, they have flagella. These are categorised into:
Autotrophs: photosynthetic autotrophs (e.g. cyanobacteria), chemosynthetic autotrophs.
Heterotrophs.
Hope this answers your question.
Good luck!