**Given,**

Inlet tap can fill a cistern in = 4 hours

Outlet tap can emptied it in = 6 hours

∵ Work done by inlet tap in 1 hour \(=\frac{1}{4}\)

∵ Work done by outlet pipe in 1 hour \(=\frac{1}{6}\)

∴ Work done by both pipe in 1 hour \(=[{\frac{1}{4}-\frac{1}{6}}]=\frac{3-2}{12}=\frac{1}{12}\)

Hence, both the tap can filled it in \(\frac{1}{\frac{1}{12}}\)=12 hours