In order for the plank to be in equilibrium, the sum of the vertical forces must be zero and the sum of the moments about any point on the plank must be zero. There are no horizontal forces.
This means the sum of the upward reaction forces at A and B must equal the sum of the downward applied forces at D and C, and the clockwise moments about any point must equal the counterclockwise moments about the same point.
For example the clockwise moments about A due to downward forces C and D must equal the counterclockwise moment about A due to the upward reaction force at B. That will be the case if the distance between C and D is 1 meter (it isn't shown in the diagram)
I don't understand principal of moments intuitively.
Think about a moment or torque as being the turning effect about a point due to the application of a force. An example is using a wrench to turn a bolt. You apply a force perpendicular to the arm of the wrench. The moment or torque is the product of your applied force and the length of the arm of the wrench between the bolt and the point where you apply the force.
Hope this helps.