Hi, this rfid module can work with 5-9V. If you have 12v solenoid and if you going to use socket at home, you need to use AC-DC power supply. You have to calculate ur circuit's amper needs. Then you can select right amper and voltage. You can buy power supply by these values for your project. So If you transfer to 230V-12V DC, you can use 12V with Arduino I guess.
| Microcontroller | ATmega328P |
|---|---|
| Operating Voltage | 5V |
| Input Voltage (recommended) | 7-12V |