Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively.

Time taken by tap A to fill the tank $=6$ hours

Time taken by tap B to fill the tank $=8$ hours

Time taken by tap C to fill the tank $=12$ hours

A fills $\frac{1}{6}$ of the tank in one hour.

B fills $\frac{1}{8}$ of the tank in one hour.

C fills $\frac{1}{12}$ of the tank in one hour.

Part of the tank filled in one hour using all the three pipes $=\frac{1}{6}+\frac{1}{8}+\frac{1}{12}=\frac{4+3+2}{24}=\frac{9}{24}$

Time taken by A, B and C together to fill the tank $=\frac{24}{9}=\frac{8}{3}=2 \frac{2}{3}$ hours