Like to/ like +ing. Like to go or like going?
Both
I like eating fruit and
I like to eat fruit are correct but they have different meanings.
I like eating fruit means that I enjoy eating fruit, when I taste an apple or an orange etc I feel good.
I like to eat fruit means that I think that it is good to eat fruit. I have read articles about a healthy diet and I see that it is better for our health to eat 5 pieces of fruit or vegetables a day
Another example:
I don’t like wearing a seat belt when I am in a car (I find it uncomfortable in hot weather, I don’t enjoy wearing a seat belt) but I like to wear a seatbelt (because if I’m involved in an accident it could save my life)
These rules can also be applied in the past.
I liked playing football in the park with my friends but I didn’t like to wear a hat when it was cold
If like is used together with a modal verb we can only use the like to model.
I would like to eat early today, I have a meeting this afternoon