How does Pascal's law apply in the case of two openings with different pressures?

Pascal's Principle states that when pressure is applied to an enclosed, incompressible fluid, the pressure change will be transmitted to all other parts of the fluid, including the walls surrounding it. So for Pascal's Principle to apply, we must have an enclosed container.

Pascal's law just says that any change in pressure at any point in an enclosed and incompressible fluid fluid is transmitted throughout the fluid.

So if the tube is open, we can't apply Pascal's law there as it requires an enclosed fluid.

Saying we have this system, close U-tube with water, two positons are exerted by external pressure $P_1$ at $B$, and $P_2$ at $A$. $P_2 > P_1$ and the water levels are diffeeed by height $h$ reflected the pressure variance.

Pascal's Law: All pressure are transmitted to all part of water. Therefore, the water in same elevetion shoud have same pressure. Otherwise, the water will not stay in equilibrium. In the figure, the point B and C have same pressure. The pressure difference between A and C equals to the difference between A and B. Therefore

$$ P_2 - P_1 = rho g h. $$

Newton's Law: At point A, the water exerts a pressure $P_1$ to balance the piston's external pressure $P_1$. Also at point $B$, the piston has pressure $P_2$ from water to balance the external pressure $P_2$.