How much is a 1964 elizabeth the second penny worth?

All coins from countries in the British Commonwealth carry a portrait of Queen Elizabeth ("Regina Elizabeth" in Latin) so that's not enough to identify the specific country that issued your penny.

However, regardless of the country it comes from, unless the coin is in almost-uncirculated or uncirculated condition it's unlikely to be worth very much. As with US cents, pennies are about the most common denomination in those countries that use them.