I've got 2 options for sentences here:
I visit my hometown about two or three times a year.
I visit my hometown about twice or three times a year.
Which one is correct and natural?
The first sentence should be..
"I visit my hometown about two or three times a year"
While in the second sentence maybe grammatically incorrect
It should be "I visit my hometown twice or thrice a year
See http://dictionary.cambridge.org/de/worterbuch/englisch/twice