Here’s a possible way to fill in the blanks:

1. **(1)** climbing
2. **(2)** build
3. **(3)** within
4. **(4)** Stay
5. **(5)** properly
6. **(6)** why

So the completed text would read:

"There are a lot of pastimes that young people like, and one of (1) **climbing** is mountain climbing. It is an active leisure activity that people can do either indoors or outdoors. If you go climbing outdoors, it is a great way to (2) **build** your strength and enjoy nature at the same time. You can even set up your own climbing wall in your backyard or (3) **within** your home. This way you don't have to go out and still can (4) **Stay** fit and enjoy the activity. So how can you start mountain climbing? Many people take a class to learn how to climb and use their equipment (5) **properly**. Others join climbing clubs to make new friends with the same interest and go climbing together. If you are an active person and like outdoor activities, (6) **why** don't you try this activity?"