If net external moment of some forces is zero about a point, then the net external force passes through the point

It means that when n number of forces are acting on a body,and if about certain point the net torque is zero (say P), then you find the net force and apply it at that point, P (in free body diagram) and you will get the same dynamics of the body as earlier.

Take a slab in space (because its easy to visualize). Now apply coplanar forces(say in xy plane). The forces should be opposite and of different magnitude. you can find a point about which the body will not rotate along z axis(P).And also calculate the torque about other points on the body(say S).

since the forces are of different magnitude, calculate the net force and in the free body diagram, apply the net force at that point where the torque is zero. calculate the torque about other points(S) and you will find that you will get the same torque (about S) as calculated earlier(about P).

For translation we always take force about COM , so translational dynamics is same in both cases, and rotation is also same in both cases(as same torque). So you will get the same dynamics.

you change the Plane from xy- to any other , the law will hold for any plane. you can apply forces in arbitrary direction,resolve those forces in x, y, z and individually find the dynamics along 3 direction, and they are independent and same (about S and P). so overall dynamics is same.Therefore the rule applies for forces in any arbitrary direction

If net external moment of some forces is zero about a point, then the net external force passes through the point

It means that when n number of forces are acting on a body,and if about certain point the net torque is zero (say P), then you find the net force on the body and apply it at that point, P (in free body diagram) and you will get the same dynamics of the body as earlier.

Take a slab in space (because its easy to visualize). Now apply coplanar forces(say in xy plane). The forces should be opposite and of different magnitude (for simplicity). you can find a point about which the body will not rotate along z axis(P) as we are applying the force in XY plane .And also calculate the torque about other points on the body(say S).

since the forces are of different magnitude, calculate the net force on body and in the free body diagram, apply the net force at that point where the torque is zero(P). calculate the torque about other points(S) and you will find that you will get the same torque (about S) as calculated earlier(about S) when the force was not translated.

For translation of body we always take force about COM , so translational dynamics is same in both cases, and rotation is also same in both cases(as same torque). So you will get the same dynamics.

you change the Plane from xy- to any other , the law will hold for any plane. you can apply forces in arbitrary direction, resolve those forces in x, y, z and individually find the dynamics along 3 direction, and they are independent and same (about S and P). so overall dynamics is same.Therefore the rule applies for forces in any arbitrary direction