Final answer:
The Mercator projection is the map projection that shows Greenland being as large as Australia due to the distortion of sizes at higher latitudes.
Step-by-step explanation:
The projection that shows Greenland being as large as Australia is the Mercator projection.
The Mercator projection is well-known for distorting sizes as latitude increases and can make high-latitude regions such as Greenland look significantly larger than they are in reality.
In contrast, Australia's size is shown much more accurately on this type of map. Other projections like the Robinson, Azimuthal, or Mollweide attempt to correct these distortions and provide a representation of countries and continents that is more proportional to their true sizes.