A can complete the work in (7*9)=63 hours
B can complete the work in (6*7)=42 hours
=> A's one hour's work=1/63 and
B's one hour work=1/42
(A+B)'s one hour work=1/63+1/42=5/126
Therefore, Both can finish the work in 126/5 hours.
Number of days of 8 2/5 hours each=(126*5/(5*42))=3days

A can do a piece of work in 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?
the question has number with factors of 3 , 2 , 7 repeatedly. So it is better not to solve them at each step
A does in 1 hr 1/ (7*9) B does in 1 hr 1/(6*7)
A + B together in 1 hr 2+3 /(7*9*2)
so in 42/5 hrs = 7*9*2*5/ 6*7*5
= 3`