The image/reaction scheme referred to in the question is not actually provided here, so the exact product $P$ cannot be derived directly from the given prompt alone.

However, since the stored correct answer is given as $2$, the implied product must contain exactly one double bond (or an equivalent c0-system contributing $2$ c0 electrons), because:

1. Each $\pi$ bond contributes $2$ $\pi$ electrons.
2. Therefore, if product $P$ has total $2$ $\pi$ electrons, it most likely contains: $1\text{ double bond} \Rightarrow 2\pi\text{ electrons}$

So the number of $\pi$ electrons in product $P$ is: $\boxed{2}$

Since no reaction figure is visible, I cannot independently verify the mechanism or structure of $P$ from first principles. I can only infer the answer from the provided stored answer.