You could argue that the abolitionist movement has impacted every decade in US history since it began. However, the answer that you are probably supposed to give is that Douglass had an impact on the 1840s, 1850s, and 1860s.
Frederick Douglass's public career started in the 1840s. His autobiography was published in 1845. His influence continued to be very important at least up through the Civil War in the 1860s. The 1840s, 1850s, and 1860s were very important decades in US history because they are the decades in which the animosity between the North and South built and finally erupted into the Civil War. Throughout that period, the abolitionist movement helped to inflame tensions between the two sections of the country and Douglass played a big part in that movement.