Can I use a 12 volt adapter for a 6 volt equipment?

No. The voltage difference is too great. There are types of adapters in the market place that have variable set point voltages. You can usually go from 1.5,3,4.5,6,7.5,9 and 12 volts with these types of wall plug in adapters.These types of adapters also come with different end type connectors for connecting to many different devices.