Solution: According to the above given formula, P and Q can do a work in x days, Q and R can do the same work in y days, P and R can do it in z days. If they all work together P, Q, R can do that work in $\frac{\mathrm{xyz}}{\mathrm{xy}+\mathrm{yz}+\mathrm{zx}}$days.

So, 

$$\begin{gathered} \frac{4\times 8\times 12}{(4\times 8)+(8\times 12)+(12\times 4)}=\frac{384}{32+96+48} \\ =\frac{384}{176}=2.18 \mathrm{days} \end{gathered}$$

Hence, if all of them work together, the work will be completed in 2.18 days 

Hence option C is correct