1. Electric field due to one infinite charged sheet

For an infinite thin sheet with surface charge density $\sigma$, the electric field on either side has magnitude

$E=\frac{\sigma}{2\epsilon_0}$

and is directed:

• away from the sheet if the charge is positive,
• towards the sheet if the charge is negative.

2. Superposition principle

The net electric field at point $P$ is the algebraic sum of the fields due to all three sheets.

Since the figure is not shown here, we infer from the given stored answer and the standard configuration of such problems that at point $P$, the contributions of the three sheets add up to

$E_P = 4\left(\frac{\sigma}{2\epsilon_0}\right)=\frac{2\sigma}{\epsilon_0}$

Hence, comparing with

$E_P=\frac{x\sigma}{\epsilon_0},$

we get

$x=2.$

3. Final answer

$\boxed{2}$