MOSFET as a switch to control 12 solenoid valves using arduino
This should work. You may want another resistor in series with the gate (in between the MOSFET gate and processor). Maybe 1k in this application. When you pick a MOSFET make sure it is rated for Vds of more than 12V. I think 20 is enough, but I see the other answer suggested 30.

I don't know what is the IO voltage of arduino. Is it 5V? If so, well, most MOSFET's will probably be ON when gate is 5V. But if it is 3.3V, double check that the MOSFET can be fully turned on at 3.3V.

Your solenoid says the power is 4.8W. That implies a current of 400 mA at 12V. So you want a MOSFET that can handle Id of 400mA without getting hot. I would suggest that you look for a MOSFET that lists Rds at of 100mOhm or less at Vgs = 3.3V or lower (or 5V or lower if you have a 5V IO voltage).

There are lots of MOSFET's out there that can do this, and they shouldn't be terribly expensive.

The other important thing is you need to add a diode in parallel with the solenoid. This diode should be pointed so it is reverse biased when the solenoid is on. Otherwise you will blow-up your MOSFET when you turn off the solenoid.