12 men can do a piece of work in 24 days. How many days are needed to complete the work, if 8 men do this work ?

12 men can do a piece of work in 24 days
$$ \Rightarrow {{\text{M}}_1} = 12{\text{ and }}{{\text{D}}_1} = 24$$
8 men can do this work in $${{\text{D}}_2}$$ days
$$\eqalign{ & \Rightarrow {{\text{M}}_2} = 8{\text{ }} \cr & \,\,\,\,\,\,\,\,\,{{\text{M}}_1}{{\text{D}}_1} = {{\text{M}}_{\text{2}}}{{\text{D}}_{\text{2}}} \cr & \Rightarrow 12 \times 24 = 8 \times {{\text{D}}_2} \cr & \Rightarrow {{\text{D}}_2} = \frac{{12 \times 24}}{8} \cr & \Rightarrow {{\text{D}}_2} = 36{\text{ days}} \cr} $$