An example of an NP-hard problem is the _Traveling Salesman Problem (TSP)_, a famous optimization problem where one needs to find the shortest possible route that visits all the cities in a given list exactly once and returns to the starting city. Another example of an NP-hard problem is the _Knapsack Problem_, where one needs to choose a subset of items from a given set of items so that the total value of the chosen items is maximized while limiting the total weight of the chosen items below a given limit.

On the other hand, an example of a P problem is the _Shortest Path Problem_, where one needs to find the shortest possible route between two vertices in a directed graph. Another example of a P problem is the _Linear Programming Problem_, where one needs to find the optimal solution to a set of linear constraints by minimizing or maximizing a linear objective function subject to the constraints.

The difference between NP-hard and P problems is that the time required to solve an NP-hard problem increases exponentially with the size of the input, whereas a P problem can be solved in polynomial time with respect to the size of the input. This means that an NP-hard problem can become infeasible to solve for large inputs, while a P problem can always be solved efficiently.

In conclusion, although both P and NP-hard problems are difficult to solve efficiently, the latter is much more difficult than the former, due to the exponential complexity and increasing computation time with respect to the size of the input. To solve an NP-hard problem efficiently, one may need to resort to approximation algorithms or heuristic methods, which can provide approximate solutions in a reasonable amount of time.
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