The answers for this question are:
a. You push a box until it moves. = unbalanced
b. You push a box but it doesn't move. = balanced
c. You stop pushing a box and it slows down. = unbalanced
As a general explanation for all the items, forces are considered balanced when they cancel each other out. This means that no net force is produced. A and C are unbalanced because one force was able to overcome the force exerted by the object.