Explanation

(b)
We have, $\left| \mathcal{z} + 4 \right| \leq 3\ \Rightarrow \ - 3 \leq \mathcal{z} + 4 \leq 3$
$\Rightarrow \ - 6 \leq \mathcal{z} + 1 \leq 0\ \Rightarrow \ 0 \leq - \left( \mathcal{z} + 1 \right) \leq 6$
$\Rightarrow \ \ 0 \leq \left| \mathcal{z} + 1 \right| \leq 6$
Hence, greatest and least values of $\mathcal{|z} + 1|$ are 6 and 0 respectively