A can do a piece of work in 24 days and B in x days. A starts the work and works for 6 days, then B joins and together they work for 2 more days to complete the work. Find the value of x.

8 

A's work of 1 day = $\frac{1}{24}$

Work done in 6 days = $\frac{6}{24}$ = $\frac{1}{4}$

Therefore, one - fourth of the work is done 

Remaining work is done by A and B together in 2 days 

A and B will complete the total work in 3 x 2 = 6 days

Efficiency of B = 4 - 1 = 3

Time taken by B alone to complete the work = $\frac{Total\; work}{Efficiency}$

                                                                = $\frac{24}{3}$ = 8 days