For this problem, the direction of traffic flow is only in one way. Thus, they say that the constraints for x1,x2,x3,x4 must be greater or equal than 0. I don't understand why having a one way road implies that the flow in each streets must be positive. why couldn't we have negative flow. Also, I wanted to ask what would happen if we would allow traffic to flow in both ways in each street ? why would that now imply that we can have negative flow? Actually I don't even know what would it mean to have negative flow. How can the flow be a negative number when its impossible to have negative amounts of car. Please help me understand this intuitively .
For each $i$, $x_i$ denotes the number of cars that went from the beginning of the road to its end over one minute; for example, $x_1$ is the number of cars that went from $A$ to $B$. Since we're counting cars, it doesn't make sense to get a negative number; $x_1 = -3$ means that "we counted $-3$ cars"; as you note, we can't have negative amounts of car.
In a setting where flow occurs in both directions, we would take $x_i$ to denote the net flow in a given direction. That is, $x_1$ would be equal to the number of cars that went from $A$ to $B$ minus the number of cars that went from $B$ to $A$. Even if this interpretation is applied, we still come to the conclusion that $x_1$ must be non-negative: the road is one-way, so no cars went from $B$ to $A$.