This is Solitaire MahJongg, a 144 tile solitaire game. The first popular Solitaire MahJongg for the PC was Shanghai released by Activision in 1988, and there have been numerous PC versions ever since. I came across a nice page of Freeware and Shareware Solitaire MahJongg, which has versions for PC, Mac, and even a Flash version.
If you're unfamiliar with Solitaire MahJongg it might seem a bit alien and intimidating at first, but the rules are surprisingly simple. The object of the game is to remove all the tiles from the board. Tiles are layered in stacks so that if you look at it from the side it looks a bit like a pyramid. The tiles are removed in pairs according to simple rules from either the left or the right side of the board. Once you've learned the rules it can be quite addictive. Not all of the Solitaire MahJongg listed on the Freeware and Shareware page are that old, but some of them are. Unfortunately the original Shanghai for DOS is protected by the ESA (formerly the IDSA) so it can't be downloaded legally. But there's plenty of freeware alternatives to choose from!