A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 days of which B has been destroying. How many days must A now work alone to complete the work?

In 6 days part of the work done by A = $frac{6}{8} = frac{3}{4}$

during 2 days, part of the work destroyed by B = $frac{2}{3}$

work done = $frac{3}{4} - frac{2}{3} = frac{{9 - 8}}{{12}} = frac{1}{{12}}$

Remaining work = $1 - frac{1}{{12}} = frac{{11}}{{12}}$

Required no of days = $= frac{{11}}{{12}} imes 8$ = $= 7frac{1}{3}$ Days