What does Qu te gusta hacer mean?

"Que te gusta hacer?" means "What do you like to do?" (the "e" in Que should carry an accent mark.)

As a result, you use the verb "gustar" for "like" and finish the answer with any type of activity that you like to do.

• I like to study. - Me gusta estudiar.
• I like to run. - Me gusta correr.
• I like to swim. - Me gusta nadar. / Me gusta la natacion.
• I like cook. - Me gusta cocinar.