**12 hours**

Pipe A can fill the cistern in 4 hours

Therefore in 1 hour pipe A can fill 1/4 of the cistern

Pipe B can empty the cistern in 6 hours

Therefore in 1 hour pipe B can empty 1/6 of the cistern

Therefore together in 1 hour they can fill 1/4 - 1/6 of the cistern

Taking LCM, (6 - 4)/24 i.e. 2/24 can be filled in 1 hour

That is 1/12 of the cistern can be filled in 1 hour

To fill the one cistern, we will need 12 hours