Contact Force Between Blocks

Because the two blocks stay in contact and the floor is smooth, they accelerate together as a single system. The common acceleration follows from Newton's Second Law applied to the combined mass: $a=\frac{F}{m_1+m_2}=\frac{20}{2+3}=4{\text{ m/s}}^2$. The contact force is the only horizontal force acting on the rear 3 kg block, so by the Second Law applied to that block alone, $F_{contact}=m_{2}a=3\times 4=12\text{ N}$. The 8 N value would be the force on the 2 kg block instead, the wrong member of the pair. The 20 N value wrongly assumes the full applied force transmits unchanged, ignoring that the pushed block also needs accelerating. The 4 N value confuses the acceleration with the force. A revealing thought experiment is to reverse the arrangement and push instead on the 3 kg block; the contact force would then become $2\times 4=8\text{ N}$, showing that the internal force depends on which block is pushed and on the mass lying ahead of the contact surface. This is the standard NCERT two-block contact-force analysis, and it embodies the Third Law because each block pushes on the other with equal and opposite contact forces. As a check, the contact force equals the mass-weighted share of the applied force, and a larger trailing block experiences a larger contact push, which holds here.