Situation 4 will never pass through the origin. Situation 2 depends on the value of the initial velocity and acceleration; the particle could possible pass through the origin, but it doesn't have to.
Work Step by Step
The particle starts off at -20m, this means that it must travel in the positive direction to reach the origin. The particle in situation 4 starts off traveling in the negative direction and continues in that direction forever so, the particle will never pass through the origin. In situation 2, the particle starts off in the positive direction but has a acceleration in the negative direction. So, depending on the values, the particle could potentially pass the origin but it doesn't have to. A low velocity and a high acceleration magnitude will cause the particle to never pass the origin. A high velocity and low acceleration, however, will surely allow the particle to pass the origin.