Thanks for your question Greg. Under section 109 of the Australian Constitution, if a state parliament and the federal Parliament pass conflicting laws on the same subject, then the federal law overrides the state law. Section 122 of the Constitution allows the federal Parliament to override a territory law at any time. Some of the areas where the federal and state or territory parliaments have made conflicting laws include the environment, health, education, heritage protection, euthanasia and same-sex marriage.
Section 71 of the Australian Constitution gives the High Court of Australia the power to resolve disagreements between the federal and state governments over their law-making powers. If a law is contested (challenged), it is up to the High Court to decide whether the Constitution gives the relevant parliament the power to make this law. A law judged by the High Court to be unconstitutional is then invalid (over-ruled). To find examples of where the High Court has found in favour of the federal Parliament, check this Closer Look paper, Governing Australia: three levels of law-making.