I want to apply for a patent that can achieve one purpose, but there are two ways. What should I do?

If your two methods are based on the same invention idea, then you can list them in the same invention application and apply together.

If these two methods are not based on the same idea, then you can only apply for two inventions. ^_^

To apply for a patent, it is not necessary to create a physical object, as long as it can clearly explain how the technical scheme of the invention is realized; If you can't even come up with the second technical scheme, I suggest you don't apply. Moreover, since you can't figure out how to realize the technical scheme, others should not, and you don't have to worry about other people's applications.