"Free time" is the time when you are free from work, school or college.
In your free time you can do different things like for example spend time with your family, go out with friends, cook a big meal, watch TV etc.
The question that we ask is usually: WHAT DO YOU DO in YOUR FREE TIME?
The answer can be: I stay at home and watch TV. or I go out with my friends. or I visit my grandmother.
There is another question which has the same meaning. WHAT DO YOU LIKE DOING in YOUR FREE TIME?
The answer can be: I like going to the desert. or I like having a picnic in the park. or I like staying at home and playing computer games.
Now, did you see the difference? When you say LIKE, after that you have to use ing verb: I like cooking, I like reading, I like sleeping, I like going.
In the next photo quiz match the name of the activity with the correct picture.