Unfortunately if you would like a very progressional finish using the same spot that the 6" light was in, there is no short cut but to remove the 6" can entirely. The question is how to make a 6" opening to be able to fit a 4 inch opening the size of the smaller light fixture. Cut a 4" opening in a piece of sheet rock meant to be in the circumference the smaller new receptacle which would be 6 1/4 in diameter.Slide the circular piece of sheet rock into the opening in the ceiling piece and with some sort of tape to hold it in place. Spackly around the newly inserted piece. After it dries sand the area,and paint. It will look as good as new.

Unfortunately if you would like a very professional finish using the same spot that the 6" light was in, there is no short cut but to remove the 6" can entirely. The question is now "how do I make a 6" opening to be able to fit a 4 inch opening the size of the smaller light fixture?". 

Cut a 4" opening in a piece of sheet rock the size of the old opening. Slide the circular piece of sheet rock into the opening in the ceiling and use some sort of tape to hold it in place.

Spackle around the newly inserted piece. After it dries, sand the area and paint. It will look as good as new.