As far as I can make out, the valve operates by changing the voltage across it. As its a solenoid (resistor), the current through it depends on the voltage. I = V/R.
You can regulate the valve by putting a resistor in series with it to reduce the voltage, but it would use a lot of power so would have to be BIG. Also it would have to be adjustable which would make it a very expensive component.
What this circuit does is to pulse (switch) the voltage on and off, if its on for 100% of the time, the valve is being fed from 12V, if the voltage is pulsed on for 50% of the time, its like the valve is being fed from 6V. if you try and measure the voltage directly, you could fool your self depending on the meter as its not a continuous 6V, but a series of 12V pulses. A few cheap components would filter the pulses enough to give you an accurate DC voltage which you can then measure.
Frank