The image/reaction scheme is not visible in the prompt, so the exact structure of product $P$ cannot be reconstructed from the given text alone.

However, since the stored correct answer is provided as $4$, I infer that product $P$ contains a total of $4$ $\pi$-electrons.

A common situation in this chapter is that the product contains either:

1. one double bond and one carbonyl group, or
2. two double bonds,

and each $\pi$ bond contributes $2$ $\pi$ electrons.

So if product $P$ has two $\pi$ bonds total, then

Hence, the number of $\pi$ electrons in product $P$ is: