Final answer:
The question incorrectly implies that freedom of the press would vary by congressional district; it does not. The First Amendment protects freedom of the press throughout the United States, applicable to all congressional districts.
Step-by-step explanation:
The situation described in the question does not pertain to any particular congressional district defined by its numerical designation (8th, 4th, 2nd, or 1st). Instead, the question touches on the broader issue of freedom of the press and its protection under the First Amendment to the US Constitution. The First Amendment guarantees that Congress shall make no law abridging the freedom of speech or of the press. Therefore, a US representative prohibiting a local newspaper from printing an editorial that is critical of her voting record would be acting in violation of these constitutional protections, regardless of which congressional district she is serving.
Such actions would likely be subject to legal challenge, and historically, the courts have upheld strong protections for the press in cases where government officials have attempted to prevent the publication of material, as seen with the Pentagon Papers (New York Times Co. v. United States, 1971). The constitutional amendment proposed by Senator Lisa Murkowski in 2009 or the strategies used by political figures to appeal to their constituencies, as mentioned in the reference materials, do not specify the congresswoman's district either, as the protection of free speech and press is vital in all congressional districts.