Yes, you can make money with a free blog. In fact, many people do make a living from their blogs. The key is to create a blog that is interesting and informative.
You also need to build an audience around your blog. Then, monetize your blog by selling advertising space or by charging for access to your content.
If you are new to blogging, it can be hard to start making money right away. However, with some effort and perseverance, you can start making a living from your blog.