A district covers more than a single municipality.
Brandenburg is the federal state; Prignitz is a district within it. Its territory includes places such as Perleberg, Pritzwalk and Wittenberge. In this question the name therefore means neither an additional federal state nor just one town.
In administrative texts, notice both the name and the territorial level. Kreisverwaltung Prignitz means the district administration. A town administration within the district is a different administrative level. A place name alone does not tell you which office handles a particular task.

The other three answers
The other three names are also districts, but outside Brandenburg.
Rhein-Sieg-Kreis
Rhein-Sieg-Kreis is in North Rhine-Westphalia. The word Kreis matches the requested territorial level, but the state does not.
Vogtlandkreis
Vogtlandkreis belongs to Saxony. A place name from eastern Germany alone does not establish that it belongs to Brandenburg.
Amberg-Sulzbach
Amberg-Sulzbach is a district in Bavaria’s Upper Palatinate. It does not belong to Brandenburg.
Similar names can identify different territories.
Prignitz and Ostprignitz-Ruppin are neighbouring but distinct districts. The extra word Ost in the second name does not make it merely an alternative spelling of Prignitz district.
The question asks only which federal state a district belongs to today. Historical regional names, tourism regions and administrative boundaries need not coincide. The official district classification is sufficient for the answer.
District territory and administrative seat · Prignitz district ↗Prignitz: a district in north-western Brandenburg.
Perleberg is the administrative seat; Prignitz is the district.
Three words for this question
- der Landkreisdistrict
- A local-government territorial unit covering several municipalities.
- der Verwaltungssitzadministrative seat
- The place where a territorial unit’s administration is based.
- die Kreisverwaltungdistrict administration
- The administration at district level.
