Complex sentence: They were assigned to suppress the local Ku Klux Klan, which had attacked freedmen and other Republicans, and to break up illegal distilleries, which began to flourish in the South after the Civil War.
Split into simpler sentences: They were assigned to suppress the local Ku Klux Klan, which had attacked freedmen and other Republicans. They also broke up illegal distilleries, which began to flourish in the South after the Civil War.