One part of the sentence has an error. Choose that part:

The correct answer is Option (3) → than going out

Prefer ... to:

• The verb prefer compares two things with "to", not "than": prefer one thing to another.
• When the two things are actions, both take the -ing form: prefer reading to going out.
• This sentence: "prefer reading than" should be "prefer reading to".
  Corrected: On Sundays I prefer reading to going out visiting my friends.
  Example: My father prefers walking to driving.

Why the Other Options are Incorrect?

Option 1: On Sundays — Incorrect. "On" is the right preposition before days of the week; this part has no error.

Option 2: I prefer reading — Incorrect. "Prefer" followed by the -ing form "reading" is correct.

Option 4: visiting my friends. — Incorrect. "Going out visiting my friends" is a correct phrase: the -ing form tells what the going out is for.