A radioactive element X 92242 emits two α -particles, one electron...

When a radioactive nucleus emits $1\alpha$-particle, its mass number decreases by $4$ and the atomic number decreases by $2$. During positron emission, the mass number remains unchanged but the atomic number decreases by $1$. Similarly, during electron emission, the mass number remains unchanged but the atomic number decreases by $1$.

So, the value of $P = 92 - 2 - 2 + 1 - 1 - 1$

$⇒ P = 92 - 5$

$⇒ P = 87$.