A 4 kg block A is placed at the top of 8 kg block B which rests on a smooth table. A just slips on B when a force of 20 N is applied on A. The maximum horizontal force F required to make both A & B move together is

When the force is applied on A, the body will slip when the friction acting between the blocks is limiting.

So the value of limiting friction is 12N....(1)

When they both move together
$\mathrm{a}=\frac{\mathrm{F}}{\mathrm{total} \mathrm{mass}}=\frac{\mathrm{F}}{12}$
From F.B.D of A,
The only force acting on A is frictional force between the blocks.

From newtons second law

$\mathrm{F}-\mathrm{f}=8\mathrm{a}$

$\mathrm{F}-\mathrm{f}=8.\left(\frac{\mathrm{F}}{12}\right)$

∴F − F​/3 = 12
F = 36N