The question relates to the time difference between two points of longitude on Earth. The time varies based on the longitude, with 15° of longitude representing a difference of 1 hour. In this case, the difference between 12:00 PM (noon) and 6:30 AM is 5.5 hours or 82.5 degrees of longitude. Since we have to move westwards from 82° 30` E to reach an earlier time, we need to subtract 82.5 from 82° 30`E.

Option 1: 165° E has the same time as 82° 30` E but it doesn`t represent 6:30 AM, therefore it is incorrect.

Option 2: 67° 30` W is located on the other side of the globe and has a time difference of almost 10 hours, not 5.5, so it is incorrect.

Option 3: 0° E or W, also known as the Prime Meridian, in reality, has a time difference of 5.5 hours from 82° 30` E which is the right answer.

Option 4: 82° 30` W has a time difference of almost 11 hours from