Australia is located in the southern and eastern hemispheres. Because the world can be split into four hemispheres based on the four cardinal directions, any given place on the planet will fit into two hemispheres.
Like any other place on earth, Australia is located within two hemispheres; all points on the planet are covered by a north/south or east/west direction. Australia is south of the Equator, the dividing line between the northern and southern hemispheres, so it is in the southern hemisphere. The Prime Meridian separates the eastern hemisphere from the western, and Australia, because it is to the east of the Prime Meridian, is part of the eastern hemisphere as well.