Lincoln and Douglas were known for what joint activity

Debates, is the right answer.

Explanation:

The Lincoln-Douglas debates were a set of seven discussions between Stephen Douglas, a candidate of Democratic Party and Abraham Lincoln of the Republican Party. It was the period, U. S. representatives were chosen by state assemblies; thus Douglas and Lincoln were working for their bodies to gain authority of the General Assembly of Illinois.

Lincoln-Douglas debates, series of seven debates between the Democratic senator Stephen A. Douglas and Republican challenger Abraham Lincoln during the 1858 Illinois senatorial campaign, largely concerning the issue of slavery extension into the territories.