The correct answer is: D. Algebraic sum of the moments of the forces about the point is zero.
A point subjected to a number of forces will be in equilibrium if the algebraic sum of the moments of the forces about the point is zero. This means that the net torque on the point is zero. If the net torque is zero, then the point will not rotate.
The other options are incorrect because they do not take into account the moments of the forces. Option A states that the sum of resolved parts in any two directions at right angles, are both zero. This is only true if the forces are concurrent, which means that they all intersect at the same point. Option B states that the algebraic sum of the forces is zero. This is only true if the forces are balanced, which means that they all have the same magnitude and opposite directions. Option C states that two resolved parts in any two directions at right angles are equal. This is only true if the forces are collinear, which means that they all lie along the same line.