Draw the free body diagram that represents the particle accelerating in positive x direction

Explanation

The relative magnitude of forces should be indicated when the free body diagram for mass m is drawn.

Case (a): The forces `F_1` and `F_2` have equal length but opposite direction. So net force along y-direction is zero. Since the force is zero, acceleration is also zero along Y-direction (Newton.s second law). Similarly in the x direction, `F_3` and `F_4` have equal length and opposite in direction. So net force is zero in the x direction. So there is no acceleration in x direction.
Case (b): The forces `F_1` and `F_2` are not equal in length and act opposite to each other. The figure (b) shows that there are unbalanced forces along the y-direction. So the particle has acceleration in the y-direction. The forces `F_3` and `F_4` are having equal length and act in opposite directions. So there is no net force along the x direction. So the particle has no acceleration in the x direction.
Case (c): The forces `F_1` and `F_2` are equal in magnitude and act opposite to each other. The net force is zero in y direction. So in y-direction there is no acceleration. The forces `F_3` and `F_4` are not equal in magnitude and `F_3` is greater than `F_4` . So there is a net acceleration in negative x direction
Case (d): The forces `F_1` and `F_2` are equal in magnitude and act opposite to each other. The net force is zero in y direction. So there is no acceleration in y-direction. The forces `F_3` and `F_4` are not equal in magnitude. The force `F_4` is greater than the force `F_3` . So there is a net acceleration in the positive x direction.