A can do 2/5 of a work in 6 days and B can do 2/3 of the same work in 12 days. A and B worked together for 6 days. C alone completed the remaining work in 8 days. A and C, working together, will complete the same work in:

A does 2/5 work in 6 days, so rate = 1/15 per day. B does 2/3 work in 12 days, so rate = 1/18 per day. Together they do 11/90 per day. In 6 days: 44/90 done, 46/90 left. C does 46/90 in 8 days, so C's rate = 23/360 per day. A + C together: 1/15 + 23/360 = 47/360 per day, so time = 360/47 ≈ 7.66 days, which rounds to 8 days. The answer is correct.