If anybody out there can help me understand what this error is and how it may have happened I would greatly appreciate it. On the reverse side of the coin it looks as if the letter t is missing from the word quarter. Any information would be greatly appreciated thank you for your time
Can you get a closeup image of the area and a shot of the obverse (front) of the coin as well? It looks like it might be a strike through (something was between the reverse die and the planchet when it was struck) or it could be damage.
In the future, try to post images with all of the background cropped away. We need to see both sides of the coin when you have a question.
It looks like a small strike through. The coin shows lots of circulation damage and wear, so it's not going to have much value over face, if any. It appears to be a real mint error, so you may want to put it in a 2x2 and add it to your collection.