A tightly-wound, long solenoid is kept with its axis parallel to a...

The magnetic field produced by a large metal sheet carrying a surface current density $K$ is given by $B_{sheet} = \dfrac{\mu_0 K}{2}$.

The magnetic field inside a long solenoid with $n$ turns per unit length and carrying a current $I$ is given by $B_{solenoid} = \mu_0 n I$.

Since the net magnetic field near the centre of the solenoid is zero, the magnetic field due to the solenoid must be equal and opposite to the magnetic field due to the metal sheet.

Equating the magnitudes of the two magnetic fields:

$\mu_0 n I = \dfrac{\mu_0 K}{2}$

$I = \dfrac{K}{2n}$