A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is:

Ratio of rates of working of A and B = 2 : 1

So, ratio of times taken = 1 : 2

B's 1 day's work = 1/12.

Therefore, A's 1 day's work = 1/6; (2 times of B's work)

(A + B)'s 1 day's work = (1/6 + 1/12)

                                 = 3/12 =1/4.

So, A and B together can finish the work in 4 days.