"Either way works for me" is a phrase that's often used to express flexibility or willingness to go along with either of two options. It's a way of saying that the person doesn't have a strong preference for one option over the other, and is happy to go along with whatever the other person or group decides.
For example, if someone asks you, "Do you want to see a movie tonight or go out to dinner?" and you respond with "Either way works for me," it means that you're open to either option and don't have a strong preference for one over the other.