A alone can complete a work in 12 days and B alone can complete the same work in 24 days.  A and B together can complete work in ___ days.

A can do work in 12 days $\Rightarrow$  Work done by A in 1 day $=\frac{1}{12}$

B can do work in 24 days $\Rightarrow$  Work done by B in 1 day $=\frac{1}{24}$

A and B can do the work in 1 day $=\frac{1}{12}+\frac{1}{24}$

$=\frac{2+1}{24}$

$=\frac{3}{24}$

$=\frac{1}{8}$

$\therefore$ A and B can complete in 8 days.