The position of the hole can be moved no more than .125" or 1/8" either up or down. Any more than this, and there is a risk that the top portion will rip when the Door Hanger is placed on the knob.
The position of the hole can not be moved left or right, only up and down. There are a few reasons for this. Firstly, the holes are cut using cookie-cutter like tools called dies that have both the hole and the slit in a fixed position. When the hole is moved up, this is done by moving the entire die up. As well, if the hole is too far off centre, the Door Hanger will actually hang crookedly.