Wiesbaden is the state capital of Hessen.

The capital is not simply the best-known city.

A city may be economically significant or very familiar from the news without being the state capital. The answer should therefore not be inferred from personal familiarity. For Hessen, the association to learn is: state capital Wiesbaden.

The Landtag provides a concrete anchor. Its official contact address is at Schlossplatz in Wiesbaden, and the city palace there forms part of the parliamentary complex. Parliament and the state government are separate institutions that both contribute to the capital’s role.

The other three answers

The other three cities are not additional state capitals of Hessen.

Distinguish a state capital, county town and federal capital.

Wiesbaden is the capital of a federal state. That does not make it Germany’s capital. Similarly, a county administration may be based in another town without making that town the state capital. The administrative level is part of the term’s meaning.

The question asks for a place name, rather than a description of the city or the name of a government member. Wiesbaden therefore remains the correct answer when the people serving in parliament or government change.