$$\eqalign{
& B = \left\{ {x \in R:\,\,\left| {x - 1} \right| < 3} \right\} \cr
& C = \left[ {m;m + 4} \right] \cr
& \left| {x - 1} \right| < 3 \cr
& \Leftrightarrow - 3 < x - 1 < 3 \cr
& \Leftrightarrow - 2 < x < 4 \cr
& \Rightarrow B = \left( { - 2;4} \right) \cr
& B \subset C \Leftrightarrow m \le - 2 < 4 \le m + 4 \cr
& \Leftrightarrow \left\{ \matrix{
m \le - 2 \hfill \cr
m \ge 0 \hfill \cr} \right. \Leftrightarrow m \in \emptyset \cr} $$
