P,Q and R can do a piece of work in 4,6 and 12 days working

P takes 4 days working 12 hrs/day to complete the job i.e. he takes 48 man-hours to complete the job.
Q takes 6 days working 12 hrs/day to complete the job i.e. he takes 72 man-hours to complete the job.
R takes 12 days working 12 hrs/day to complete the job i.e. he takes 144 man-hours to complete the job.

Taking the LCM of the total man-hours, let us say that the total work was 144 units.

If P completes 144 units in 48 hours, then P completes 24 units in 8 hours (by unitary method).
If Q completes 144 units in 72 hours, then Q completes 16 units in 8 hours (by unitary method).
If R completes 144 units in 144 hours, then R completes 8 units in 8 hours (by unitary method).

So on days 1 and 2, we have
First 8 hours (P) - 24 units
Next 8 hours (Q) - 16 units
Last 8 hours (R) - 8 units
Total - 48 units per day, so 96 units completed in 2 days.

Now, P leaves after day 2 while Q and R continue working alternatively. So on day 3, we have
First 8 hours (Q) - 16 units
Next 8 hours (R) - 8 units
Last 8 hours (Q) - 16 units
Total - 40 units per day

So, we have 136 units completed in 3 complete days and require 8 more hours to complete the task.

On day 4, resuming from who did the work last, we have
First 8 hours (R) - 8 units

So we have completed the task and taken 3 complete days and 8/24 => 1/3rd of the 4th day.

So total days taken => 3 + 1/3 = 10/3 days. Hence, Option A is the right choice.