A county brings several municipalities together.
Main-Taunus-Kreis names the county, rather than an individual town. Hofheim is one of its towns and also the seat of the county administration. The municipality of Kriftel and the town of Eschborn belong to it too. These terms therefore describe different territorial and administrative levels.
The county administration handles responsibilities for the county; its service portal lists vehicle registration, for example. The individual towns and municipalities also have their own duties. When looking for an authority, check both the place and the specific matter.

The other three answers
The other names are real counties, but in other states.
Ammerland
Ammerland is in Lower Saxony. Even a familiar county name must be matched to the correct federal state.
Altötting
Altötting is in Bavaria, so it does not answer the question about a county in Hessen.
Prignitz
Prignitz is in north-western Brandenburg. The county is not part of Hessen.
County and state capital mean different things.
Hofheim is Main-Taunus-Kreis’s county town. The capital of the whole federal state of Hessen is Wiesbaden. An administrative seat at county level does not become a state capital because of that role.
In everyday German, Kreis can also mean a geometric circle. This question concerns an administrative unit. The English word district here means a county, rather than any neighbourhood within a town.
Twelve towns and municipalities · Main-Taunus-Kreis ↗Main-Taunus-Kreis → Hessen; county town → Hofheim.
Connect the county name with a specific municipality such as Kriftel or Eschborn to make the association concrete.
Three words for this question
- der Landkreiscounty
- A local territorial unit containing several towns and municipalities.
- die Kreisstadtcounty town
- The town where the county administration is based.
- kreisangehörigbelonging to a county
- A town or municipality forms part of a county.
