Question

How did the Harding administration respond to growing public fears of communists and anarchists?

by using propaganda to convince the public that everything was under control
by using the U.S. military to break up strikes believed to be the result of foreign agitators
by conducting public hearings to expose communists working for the federal government
by empowering the Justice Department to take broad measures to arrest and deport radicals

Answer 1

The Harding administration responded to growing public fears of communists and anarchists by empowering the Justice Department to take broad measures to arrest and deport radicals.

Answer 2

During the administration of president Warren G. Harding, The Red Scare--the public fears of communists and anarchists--was widespread. The previous administration had tried to deal with it by conducting the Palmer Raids, an attempt to find and capture communists and anarchists. Even though about 3,000 people were arrested during those raids, it did not stop the Red Scare from growing.

Harding was elected with the promise of restoring normalcy to the country. At the time, despite the controversies during his administration, he was very popular. Perhaps because of his past as a publisher and newspaper editor, he  also had a great relationship with the press. Among other actions, such as staying away from international affairs and lowering taxes, he was giving news conferences regularly. So by using propaganda to convince the public that everything was under control, Harding was able to restore some of the normalcy he had promised.