According to the question,

In 1 day,

(A+B) together can complete $\frac{1 }{8}$^th of the work

B can complete $\frac{1}{12}$^th of the work

∴ A can complete the work$=\frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}$

So, A can complete the work in 24 days.

Now, B's 4 day's work$=\frac{4}{12}=\frac{1}{3}$

Remaining work$=1-\frac{1}{3}=\frac{2}{3}$

As, time taken by A to complete the work= 24 days

∴ Time taken by A to do $\frac{2}{3}$ of the work $=\frac{2}{3}\times 24=16$days

Hence option A is the correct.