Preservation is a way to make something last a lot longer than it normally would. People preserve fruit and meat so that it lasts more than a few days and they can safely eat it later.
You preserve ideas by writing them down.
You prick something when you make a hole in it with something that has a sharppoint. The person in the picture has pricked their finger with a caltrop.
You procrastinate when you delay something until later. Procrastination is only caused by yourself, unlike a delay you cannot be procrastinated by an outside influence like bad weather. Students often procrastinate doing their assignments.
When you pull something it moves towards you. When you push something it goes away from you.
The little girl in the picture is pulling a wagon behind her.
You punch something when you hit it with your fist.
People punch each other when they fight or they punch inanimate objects like walls when they are frustrated.