Suppose the original segment of wire is stretched to 12 times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?

The linear charge density id defined as the charge per unit length.

Let q be the charge and L be the length of the wire.

So, the linear charge density is

λ = q / L

If the length is 12 times, then charge should also be 12 times to keep the linear charge density same.