Two examples of push force are as follows:

1) A chair at rest is pushed to move it from one room to another. This changes the state of motion of the box.

2) A player pushes a ball using his cricket bat. This changes the state of motion of the ball.

Two examples of pull force are as follows:

1) Rope is pulled to draw water from a well. This changes the state of motion of the water bucket.

2) A darwer of a desk is pulled to open it. This changes the state of motion of the drawer.