According to the question,

Let A,B and C take x, $\frac{x}{2}$ and $\frac{x}{3}$ days, respectively to complete the work.

So, in 1 day (A+B+C) will complete

$=\frac{1}{x}+\frac{2}{x}+\frac{3}{x}=\frac{6}{x}$^th of the work.

from question, $\frac{6}{x}=\frac{1}{2}$

[As (A+B+C)'s 1 day work =$\frac{1}{2}$]

⇒ x=12

∴ Time taken to complete the work by

A= 12 days

B= $\frac{12}{2}=6$ days

C= $\frac{12}{3}=4$ days

Hence option A is the correct .