Can I control 4 DC Brushless motors with arduino uno and Adafruit motor shield?
You don't need the motor shield at all. The motor you link to has its own driver built in.

According to the connection table on the page you link to:


Red wire to +24V
Green wire is for sensing the RPM - you can ignore it
Yellow wire is the direction select - connect to any GPIO
Black wire is ground - connect to 24V GND and Arduino GND.
Blue wire is PWM control. Connect to any PWM output on the Arduino


Note that the motor will probably spin immediately power is applied until your sketch tells it to stop by driving the PWM output LOW (or 0% duty cycle).  There appears to be a 15-25kΩ (typical) pullup resistor on that pin, so adding a smaller pulldown resistor (say 1kΩ) on it should force it to be off until you turn it on.