Activities: [(1,4), (3,5), (0,6), (5,7), (8,9), (5,9)]. One possible selection: (1,4), (5,7), (8,9). These do not overlap. Count: . Can you do better? Try other combinations.
Notice that (0,6) is long and blocks many others. Avoiding it might be better. After trying, you should find that is the maximum. But how do you find this systematically? Trying all subsets takes time, too slow. You need a greedy strategy that works in polynomial time.