Answer
a) $0\;\rm V/m$
b) $0.04\;\rm V/m$
Work Step by Step
We know that the strength of the induced electric field inside a solenoid is given by
$$E_{\rm solenoid}=\dfrac{r}{2}\left| \dfrac{dB}{dt} \right|$$
Plug the known;
$$E_{\rm solenoid}=\dfrac{r}{2}\left| -4.0\right|$$
$$E_{\rm solenoid}=2r\tag 1$$
$$\color{blue}{\bf [a]}$$
On the axis of the solenoid means at $r=0$.
Plug into (1),
$$E_{\rm solenoid}=2(0)=\color{red}{\bf 0}\;\rm V/m$$
$$\color{blue}{\bf [b]}$$
Here $r=2$ cm.
Plug into (1),
$$E_{\rm solenoid}=2(0.02)=\color{red}{\bf 0.04}\;\rm V/m$$