They have fun ______(listen) to the loud music.

have fun doing sth. 开心地做某事
没有have fun to do sth结构。如：The kids are having fun playing in the park now.

那么就是listening了。

to listen

have fun doing sth. 开心地做某事

listenning
是have fun doing sth句型
have fun (in) doing sth．开开心心做某事
类似还有have problems（in）doing sth．做某事有困难

problem后接动词－ing形式，其前的介词in可以省略。如：

They had no problem（in）fixing the car．

listening
have fun doing sth