A 4kg box is initially sitting at an horizontal floor with a Coefficent of stable friction miu=04. a horizontal pushing forces is applied to the box What is the maximum pushing force that can be applied with out moving the box?

By Newton's second law, the net vertical force on the box is

∑ F[vertical] = n - mg = 0

where n = magnitude of normal force and mg = weight of the box. It follows that

n = mg

so that static/stable friction has a maximum magnitude of

f = µn = 0.4 mg

The box stays at rest up to the point that the applied force matches this magnitude of about 0.4 (4 kg) g ≈ 16 N.