What famous British explorer discovered Australia and the Hawaiian islands?

There is no answer to this question.

It is a common misconception that Captain James Cook (or Lieutenant, as he was then) of England discovered Australia. He did not. Australia was actually formally discovered by Dutch explorer Dirk Hartog in 1616. British explorer Captain Cook was the first to sight and chart Australia's eastern coast.

However, Captain Cook did discover the Hawaiian Islands, which he originally called the Sandwich Islands.