An object rests on a horizontal floor. the coefficient static friction is0.4 and acceleration of gravity is 9.8m/s

determine the maximum force of the static friction and the minimum force of F

first of all since the value of mass of the object and force F (horizontal) or the relation between them is not mentioned, so there can be multiple effects and let us study them in cases.

Let us consider that mass of the object is m and the coefficient of friction is the coefficient of static friction of the surface{since friction can be static as well as dynamic} whose value (μ) as is given in the question is 0.2. Since the surface and the force applied are both horizontal so there will be no vertical component of the force applied which means that the normal force is N=weight of the object=mg where g is the acceleration due to gravity (9.8 m/s^2 on average on surface of earth).

Case 1:

When F<=μN. This means that when the value of F is less than or equal to μN then the static friction is equal to F. So the body remains stationary.

Case 2:

When F>μN. This means that when the value of F is greater than μN then the static friction is less than F. So the body starts moving and if the force applied F is constant then the body will start accelerating because coefficient of kinetic friction is less than that of static friction.