According to the formula, If person P can do a work in x days and person Q can do the same work in y days then, one day work of P and Q together is $\frac{\mathrm{xy}}{x+y}$

so, $\frac{6\times 12}{6+12}=\frac{72}{18}=4 \mathrm{days}$

Hence, is both of them work together, work will be completed in 4 days

Hence option B is correct