Catalysis of the reaction: (9Z,12Z)-octadecadienoyl-CoA + 2 Fe(II)- + 2 H+ + O2 = (6Z,9Z,12Z)-octadecatrienoyl-CoA + 2 Fe(III)- + 2 H2O. Can also use a substrate with 3 double bonds (a (9Z,12Z,15Z)-octadecatrienoyl-CoA and add a fourth double bond (a (6Z,9Z,12Z,15Z)-octadecatetraenoyl-CoA).
delta(6)-desaturase activity