Would have been easier if you gave the part number. I suggest you check the data sheet for minimum pull in voltage. You may get a 28 volt DC coil to pull in at 24 volts but not going to happen at 12 volts. When you say 8 pin I assume DPDT contacts as in the Omron MK2 series? They are 8 pin octal base. Overall if you want a relay to work at 12 VDC you buy a 12 VDC coil relay, if you want it to work at 24 VDC you buy a 24 VDC coil relay. A 28 VDC coil will not for example work at 12 VDC. Again, provide the complete Omron part number and research the data sheet for minimum pull in for the relay you have and hope it has the data.
Ron