What does category RE6 mean on green card?

It is unimportant (most of the time) government crud.

It means:

• RE6 Refugee who entered the United States on or after Apr. 1, 1980. Sec. 209(a) of the INA as added by PL-96- 212 (Mar. 17, 1980)- ((Adjusted status))

To find this I googled: RE6 Green Card