In total, there are four forces acting on the box. Let's discuss each one of them one by one.
1.
Muscular force- The boy is using his muscles to push the box in forward direction. So muscular force is acting on the block towards the right. Muscular force is a kind of contact force(getting exerted due to physical contact between hands and the box).
2.
Friction- Force of friction is coming into play as the boy is trying to move the box towards the right. Friction acts towards the left(opposite to the direction of motion of the box). Since the box and the floor on which it is kept are physically in contact with each other, frictional force between them will definitely be a contact force.
3.
Gravitational force- Force of gravity is acting in the downward direction(towards the earth). It is a non-contact force. Even though here the box is in contact with the surface of earth, but since gravitational force can act with or without contact, it is a non-contact force.
4.
Normal Force- A force equal in magnitude and opposite in direction to that of the force of gravity, acts on the box in upward direction. This force is the normal reaction force exerted by the earth on the box to balance the force due to the weight of the box. Normal force is also a kind of contact force.
Therefore, out of the four forces , three (muscular, frictional and normal force) are contact forces whereas the remaining one(gravitational force) is a non-contact force acting on the box.