Well first of 600DPI, is 600*600 (Square)
That means if you change it to 300DPI, it is 300*300 (Square)
(300*300)/(600*600)=1/4
Therefore, if 600DPI has an image size of 16MB, as it the other image has 1/4 of the information.
You would go 16 * 1/4 =4MB