The Habsburg Empire, also known as the Austrian Empire or the Austro-Hungarian Empire, ruled over several territories during its existence. The correct answer is option D, which includes both Austria and Hungary. Let's delve into the details of these territories:

1. Austria:
Austria was the core territory of the Habsburg Empire. It encompassed present-day Austria, Czech Republic, and parts of Slovenia, Slovakia, Croatia, and Italy. The Habsburgs established their rule over Austria in the 13th century and gradually expanded their influence over neighboring regions.

2. Hungary:
Hungary was another significant territory ruled by the Habsburg Empire. The Habsburgs gained control over Hungary in the 16th century and incorporated it into their empire. The Kingdom of Hungary included present-day Hungary, parts of Slovakia, Croatia, Romania, Serbia, and Ukraine.

3. Bohemia and Moravia:
Bohemia and Moravia, located in present-day Czech Republic, were also part of the Habsburg Empire. These territories were acquired by the Habsburgs in the 16th century and played a crucial role in the empire's administration and cultural development.

4. Transylvania:
Transylvania, which is now part of Romania, was under Habsburg rule from the late 17th century. It was an important territory due to its strategic location and rich natural resources.

5. Lombardy and Venetia:
Lombardy and Venetia, located in present-day Italy, were also part of the Habsburg Empire. These territories were acquired during the Napoleonic Wars and remained under Habsburg control until the mid-19th century.

6. Galicia and Lodomeria:
Galicia and Lodomeria, situated in present-day Poland and Ukraine, were part of the Habsburg Empire. These territories were acquired in the late 18th century and played a significant role in the empire's economic and agricultural development.

7. Croatia and Slavonia:
Croatia and Slavonia, located in present-day Croatia, were also under Habsburg rule. These territories were initially part of the Kingdom of Hungary and came under direct Habsburg administration in the 18th century.

8. Other territories:
Besides the aforementioned territories, the Habsburg Empire also ruled over various smaller regions, including parts of Slovenia, Slovakia, Serbia, Bosnia, and Herzegovina.

In summary, the Habsburg Empire ruled over a vast array of territories, including Austria, Hungary, Bohemia, Moravia, Transylvania, Lombardy, Venetia, Galicia, Lodomeria, Croatia, Slavonia, and several other smaller regions. These territories formed a diverse and multi-ethnic empire that lasted for centuries before its dissolution in the aftermath of World War I.