Imagine that you have a slightly difficult situation in life. For example, imagine that you and your spouse both work long hours and also have to take care of your children. If you try hard to live with the problem, you are "making it work".
Another example is when you're negotiating with a client. The client asks for you to finish a job in one week. That's too short, so you ask for more time. The client suggests 10 days. That's still short, but you think it will be OK. So you say:
Yeah, OK. I think I can make that work.