If the correction as described in the comments is taken to be true, then you can prove that $P_1, B$ and $P_2$ are collinear. (Sketch it out and first prove that $ABP_1$ is a right angle.)

After proving this, you can reason that a maximum of three of the six points can lie on a circle.

If the correction as described in the comments is taken to be true, then you can prove that $P_1, B$ and $P_2$ are collinear. (Sketch it out and first prove that $ABP_1$ is a right angle.)

After proving this, you can reason that a maximum of four of the six points can lie on a circle.