“Elected” does not always mean “directly elected by the people”.
Several of the listed offices are filled by an election. The decisive point is therefore not merely the word elect, but who casts the votes. In a Bundestag election, eligible citizens do so; in a chancellorial election, Bundestag members vote.
Directness means there is no electoral college making a further personal choice of parliamentary members after citizens vote. Parties may nominate candidates and lists, but the parliamentary result follows from the ballots cast and the statutory rules.
The other three answers
For each office, identify the body that elects it.
the Federal Chancellor.
Under Article 63, the Chancellor is elected by the Bundestag. Citizens influence its composition, but their ballots do not replace that parliamentary vote.
the Minister-President of a federal state.
Minister-Presidents are elected by their respective state parliaments, not directly by the entire electorate. Bavaria’s constitution expressly illustrates this procedure.
the Federal President.
The Federal Convention elects the Federal President. It comprises Bundestag members and an equal number of members chosen by state parliaments.
Indirect election can also have democratic legitimacy.
The wrong options are not wrong because those offices are undemocratic. They do not match the question about direct popular election. The constitution assigns different electoral functions to different bodies.
In this particular election, “the people” means those entitled to vote under electoral law. Not every resident may participate in every election. State parliaments also have their own elections; the question does not imply that Bundestag elections are the only elections.
Article 38 · Basic Law ↗People → Bundestag. Bundestag → Chancellor.
Always ask who casts a vote in this particular election. For the direct popular election asked about here, the answer is the Bundestag.
Three words for this question
- die unmittelbare Wahldirect election
- An election without an intervening electoral college making a further choice.
- das Wahlorganelecting body
- The body casting votes in a particular election procedure.
- die BundesversammlungFederal Convention
- The special body electing the Federal President.