Hmmm, picture shows green, blue, yellow wires.
-DId this bike ever work for you or did you get it used?
-Is there a LED or LCD unit on the handlebars that indicates you have the bike turned on?
-What's not working, Is it a non working throttle or is it a pedal assist that's dead?
-Does the battery have a voltage marked in it? What is the voltage?
If ALL you have is three wires going to the motor, Yellow, Blue, Green, that indicates this is a three phase motor without sensors. There's very little that can be checked with a multimeter unless it can do this.
Sensors would require 5 more wires, smaller and colored red, black, yellow, blue, green. The first two would be 5 volt power, The last three are position sensors so the controller knows when to deliver the above three voltages. If the motor has those wires,( and you didn't show the picture), when you open it all you see for electrics will be a little circuit board holding three sensors.
First test. The wheel should spin freely forward with nothing connected. If it soins the same in reverse, it's a direct drive motor. If you feel a little more resistance in reverse, and hear gears turning, it's a geared motor. Now with the motor cable disconnected, if you touch the blue-green, yellow-blue, green-yellow, the wheel will be harder to turn in reverse each time you do it. That's a simple test of the coils. Then connect the cable and turn the wheel in reverse again. It should have the same resistance as without cable, unless the controller has a short circuit.
Another test is checking resistance, blue-green, green-blue, and yellow-blue. About 0 ohms for all three.