Being the capital is a political designation.
A state capital is the capital city of a federal state. For Schleswig-Holstein, that is Kiel. A well-known city or an important administrative seat at another level is not automatically the correct answer.
Schleswig-Holstein’s Landtag is based in the State House in Kiel. Its location on Kiel Fjord provides additional geographical orientation. The test still asks for the name Kiel, not a building or a description of the coast.
The other three answers
All three other names are towns or cities in the state, but not its capital.
Husum
Husum is the administrative seat of Nordfriesland county. That is a county role, not the role of capital of the whole federal state.
Flensburg
Flensburg is an independent city in Schleswig-Holstein. Being independent of a county does not mean being the state capital.
Lübeck
Lübeck is also an independent city in Schleswig-Holstein. Its prominence does not make it the current state capital.
City administration and state politics remain different levels.
Kiel also has its own city administration and municipal politics. Its role as state capital does not erase that local level. City and state can exercise separate responsibilities in the same city.
The illustrations are invented learning images with a city model and a discussion scene. They depict neither a verified Kiel building nor the actual State House. The location is established by the linked sources.
State House in Kiel · Schleswig-Holstein Landtag ↗Schleswig-Holstein → Kiel. Nordfriesland → Husum.
Remember state capital and county administrative seat separately.
Three words for this question
- die Landeshauptstadtstate capital
- The capital city of a federal state.
- die Fördefjord-like inlet
- A long sea inlet, such as the one at Kiel.
- das LandeshausState House
- Here, the name of the building where the Landtag works.