we know that vector products are non-commutative. How can we find the right direction? e.g consider magnetic force direction i-e., F= q V × B. Why we can not write F= q B × V? How can we find the right order?
The “right-handed” direction of the cross product is just a convention, related to the biological accident that more people are right-handed than left-handed. You could equally well use a left-hand rule and the Lorentz force would be $\mathbf F=q\mathbf B\times\mathbf v$. There is no correct order, just a conventional handedness and a conventional order.
By the way, the direction of the magnetic field could also be taken to be the reverse of the conventional direction, since the Biot-Savart law expresses it as another vector product. But when computing the force between two currents, the arbitrariness in these two vector products “cancel” and give a non-arbitrary direction for the force: parallel currents attract and anti-parallel currents repel. Here is where the math has to match the physics, with no ambiguity in directions.