I'm Australian, that screenshot is from the State election in South Australia, it is an example of how the Upper House ballot paper looks, it is similar in my state New South Wales.

The vertical columns (labelled as Group A to E in screenshot) divide up the political parties. The Greens will be one column, Labor Party another, Liberal Party another column and so on.

There are two horizontal rows separated by a thick line.

You can choose to either vote "above the line" or "below the line" but not both methods.

Above the line is used if you would like to vote based upon the wishes of a political party and below the line is used for "finer grained" voting for individual persons.

For example the Labor party might have 3 Candidates "Fred", "Mary" and "Bob" if I vote above the line I can put a 1 next to the Labor party and then the Labor party's wishes will determine how my vote is distributed.

Or if I Vote below the line I must number 12 different people in the order I want them to be chosen. So I could number Bob from Labor first, Peggy from the Greens second, then Fred from Labor third and so on and I exert exact control over how I want my preferences to be distributed.

edit: Our elections are staggered, The State parliament is elected on different day to the Federal Parliament, which is different to Local City Council elections.