A long solenoid carrying a current produces a magnetic field B...

Magnetic field due to long solenoid along its axis is given as,

$B = {\mu}_{0}nI$, where $n$ is the number of turns in the solenoid per unit length, $I$ is current in the solenoid and ${\mu}_{0}$ is a constant called the permeability of free space.

$⇒ \dfrac{{B}_{1}}{{B}_{2}} = \dfrac{{n}_{1}{I}_{1}}{{n}_{2}{I}_{2}}$

According to the question, ${n}_{2} = \dfrac{{n}_{1}}{2}\text{and}{I}_{2} = 2{I}_{1}$

$⇒ \dfrac{B}{{B}_{2}} = \dfrac{{n}_{1}}{\left(\dfrac{{n}_{1}}{2}\right)} \times \dfrac{{I}_{1}}{2{I}_{1}} ⇒ {B}_{2} = B$; means, the magnetic field remains the same.