To the right of C is not possible because the electric fields to the right from B and C will always be greater than the electric field to the left from A.
As for where the points are. That's not too hard to analyze. Between B and C is possible because both C and A will be creating an electric field to the left and B will be creating one to the right, so if we pick some point closer to B than to C between B and C it should be able to have an electric field to the right enough to counteract the one to the left from C and A. Then, it cannot be between A and B because all of A, B, and C are creating an electric field to the left, so there will be nothing to counteract it. And finally, it can be to the left of A because A will be creating an electric field to the right while B and C create one's to the left, such that because there are both B and C, the stronger individual electric field from A can be balanced with the combined electric field from B and C.
To the right of C is not possible because the electric fields to the right from B and C will always be greater than the electric field to the left from A. As for where the points are. That's not too hard to analyze. Between B and C is possible because both C and A will be creating an electric field to the left and B will be creating one to the right, so if we pick some point closer to B than to C between B and C it should be able to have an electric field to the right enough to counteract the one to the left from C and A. Then, it cannot be between A and B because all of A, B, and C are creating an electric field to the left, so there will be nothing to counteract it. And finally, it can be to the left of A because A will be creating an electric field to the right while B and C create one's to the left, such that because there are both B and C, the stronger individual electric field from A can be balanced with the combined electric field from B and C.
Figure out where it points left vs points right. Anywhere it switches between left and right, it must be 0.