Figure $($a$)$ shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure $($b$)$ gives the radial component $\backslash ($ E $\backslash )$ of the electric field versus radial distance $\backslash ($ r $\backslash )$ from the common axis, and $\backslash ($ E$\_\{$s$\}=3\mathrm{.}0\backslash$times $10^\{3\}\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$C$\}\backslash ).$ What is the linear charge density of the shell?

$\backslash (\backslash$times $\backslash$mathrm$\{$C$\}/\backslash$mathrm$\{$m$\}\backslash )$

Did you use the derived expression for the electric field produced by a long line of charge? Do you see that inside the shell, the only charge enclosed by a cylindrical Gaussian cylinder is that on the solid cylinder? Similarly, outside the shell, the enclosed charge is the combined charge of solid cylinder and shell.