To complete a piece of work A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C will take :

Given (A+B)'s one day's work = $$\frac{1}{8}$$
(B + C)'s one day's work = $$\frac{1}{{12}}$$
(A + B + C) 's 1 day's work = $$\frac{1}{6}$$

Work done by A, alone= (A + B + C) 's 1 day's work - (B + C)'s one day's work
$$ = \frac{1}{6} - \frac{1}{{12}} = \frac{{2 - 1}}{{12}} = \frac{1}{{12}}$$
Work done by C, alone = (A + B + C) 's 1 day's work - (A + B)'s one day’s work
$$ = \frac{1}{6} - \frac{1}{8} = \frac{{4 - 3}}{{24}} = \frac{1}{{24}}$$
⇒ (A + C)’s one day’s work
$$\eqalign{ & = \frac{1}{{12}} + \frac{1}{{24}} \cr & = \frac{{2 + 1}}{{24}} \cr & = \frac{3}{{24}} = \frac{1}{8} \cr} $$
⇒ (A + C) will take 8 days to complete the work together