Pipes A and B can fill a tank in 8 hours and 12 hours respectively whereas pipe C can empty the full tank in 6 hours. A and B are opened for 3 hours and then closed and C is opened instantly. C will empty the tank in:

given information, 

A fills a tank in 8 hours and B fills the same tank in 12 hours

 where as C empty the same tank in 6 hours

so work done by A in one hour will be

A does 1 work in 8 hours so work done in 1 hour is $$\frac{1}{8}$$

similarly work done by B in one hour is $$\frac{1}{12}$$

work done by C in one hour $$\frac{1}{6}$$

therefore work done by A and B together in three hours is $$\frac{3}{8}$$ + $$\frac{3}{12}$$ = $$\frac{5}{8}$$

 so time required by C to empty $$\frac{5}{8}$$ portion of tank is $$\frac{5}{8}\div\frac{1}{6}$$

                                                                                                     = $$\frac{15}{4}$$

                                                                                                      =3$$\frac{3}{4}$$