Need help with power supply in my project
It's not clear why you would need to use a battery and not a mains operated 12V DC power supply.

An unregulated 12V DC 3A power supply should suffice for the solenoids, considering that you require to energise only one solenoid valve at a time.

You would also require three 4 channel relay modules, to be driven by the Arduino outputs.



The wiring for one solenoid valve is shown. The others would be wired identically.