Albert Barnes Commentary Jeremiah 36:6

"therefore go thou, and read in the roll, which thou hast written from my mouth, the words of Jehovah in the ears of the people in Jehovah`s house upon the fast-day; and also thou shalt read them in the ears of all Judah that come out of their cities." — Jeremiah 36:6 (ASV)

The fasting day - A fasting day. Baruch was to wait for a proper opportunity (Jeremiah 36:9).