(i) Ohm's Law: The electric current flowing through a conductor wire is directly proportional to voltage difference across the conductor wire if there is no change in physical condition (temperature, length, area of cross section etc.) of wire.
(ii)
Volume of metal wire remains same.
$$
\begin{aligned}
\because \mathrm{A}_{1} l_{1} &=\mathrm{A}_{2} l_{2} \\
\frac{l_{2}}{l_{1}} &=\frac{\mathrm{A}_{1}}{\mathrm{~A}_{2}} \\
\mathrm{R}_{1} &=\rho \frac{l_{1}}{\mathrm{~A}_{1}}
\end{aligned}
$$
New resistance,
$$
\begin{aligned}
\mathrm{R}_{2} &=\rho \frac{l_{2}}{\mathrm{~A}_{2}} \\
\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}} &=\frac{l_{2}}{\mathrm{~A}_{2}} \times \frac{\mathrm{A}_{1}}{l_{1}}=\frac{l_{2}}{l_{1}} \times \frac{l_{2}}{l_{1}} \\
\mathrm{R}_{2} &=\left(\frac{l_{2}}{l_{1}}\right)^{2} \mathrm{R}_{1} \quad\left[\because l_{2}=2 l_{1}(\text { Given })\right] \\
&=\left(\frac{2 l_{1}}{l_{1}}\right)^{2} \mathrm{R}_{1} \\
\mathrm{R}_{2} &=4 \mathrm{R}_{1} \\
&=4 \times 6 \\
&=24 \Omega
\end{aligned}
$$
