Is it easier to remove a nail from a board using a hammer if the nail is closer to the hammer handle or farther away?

Hammers are commonly used to pound nails into a given material. A hammer claw is used to remove nails from a given material. The idea is to hold the nail in the hammer claw and pull it by either using a continuous sideways rocking motion (while simultaneously pulling it out), or using a support to pull it out directly. 

How far the nail should be from the handle end is an example of how we can use levers to maximize work with minimum effort. Think of a seesaw. A lighter person can balance a relatively heavy person by being as far away as possible from the fulcrum (the center pivotal point). The same is the principle here. The further the load end is from the effort end, the lesser effort is needed. Thus, we should ideally keep the nail as far away from the handle end as possible. One can also think of the different efforts needed to put a nail in when holding the hammer near the handle end or near the hammer end.

Hope this helps.