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:

(A, B, C), In 1 day, do 1/6 part of work.
(A, B), In 1 day do 1/8 part of Work.

So, (A + B + C) - (A + B) = C do in 1 day (1/6 - 1/8) part of work.
= (4 - 3)/24
= 1/24

Again, (B + C), In 1 day, do 1/12 part of work.
Therefore,
(A + B + C) - (B + C) = A, in 1 day, do (1/6 - 1/12) part of work.
= (2 - 1)/12
= 1/12

So, (A + C), In 1 day, do (1/24 + 1/12)
= (1 + 2)/24
= 1/8

So, A + C can do a job in 8 days.