It's tough to tell from the picture.
The Denver coin comes very nice in the mint set and Gems are fairly "common". Look at the shield on the reverse. If it is very clean then the coin may be very high grade.
These sets have a paper outer envelope with two plastic packages inside; one red striped and one blue striped. Typical sets go for about $4 but high grade coins can bring much more. The Denver minted coins are usually much better quality.
Time don't fly, it bounds and leaps.