Influence is not the same as state authority.
A newspaper report can start a debate. It does not enact a law, issue an administrative decision or deliver a court judgment. This is the distinction the question tests.
The media are sometimes figuratively called the fourth estate. This describes their public scrutiny role. It does not add another branch of state power to the constitutional system.
The other three answers
The other three answers belong to the separation of state powers.
Legislation
Lawmaking is the legislative branch. It establishes statutory rules.
Government
Government belongs to the executive branch, which also includes public administration.
Judiciary
The judiciary exercises judicial power. Courts decide legal disputes according to law.
Public importance does not make the media an authority.
Even a highly influential newsroom does not thereby acquire governmental command powers. Conversely, government press releases are not the same as independent journalistic scrutiny.
Press freedom does not remove legal responsibility. The limits established in Article 5 still apply.
Article 20 · Basic Law ↗Three state powers; the press observes them.
“Fourth estate” is a metaphor for scrutiny, not an additional authority.
Three words for this question
- die Legislativelegislature
- The lawmaking branch.
- die Exekutiveexecutive
- Government and administration as the executive branch.
- die Judikativejudiciary
- The branch that administers justice.