The power supply has a voltage of 12VDC when it has a load of 1A. Its voltage might be 15VDC when it has a low load current like your item.
Your item operates from four battery cells so the total voltage is only 6V.
If you use a 6V regulator to reduce the 15V to 6V then it will probably get very hot and might melt, shut-down or smoke.
The datasheet of every voltage regulator shows an input capacitor, an output capacitor and a formula showing how much cooling it needs.