A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

$$\eqalign{ & \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{6} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{8} \cr & \left( {{\text{B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{12}} \cr & \therefore \left( {{\text{A + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {2 \times \frac{1}{6}} \right) - \left( {\frac{1}{8} + \frac{1}{{12}}} \right) \cr & = {\frac{1}{3} - \frac{5}{{24}}} \cr & = \frac{3}{{24}} \cr & = \frac{1}{8} \cr }$$
So, A and C together will do the work in 8 days