I was wondering if anyone knows what this game is. It has 59(maybe missing 1) pegs that are red on one side and wood color on the other. It is a 12 x 8 Pegboard Game. There are no markings on the inside or outside and it folds like a briefcase. Everything is made of wood except the handle, rubber feet, and latches.
your pegboard looks like an earlier or a later edition of the plastic pegboard we have at the psychology museum. 
All pegs have two colors like yours. Among other things these and other pegboards were developed for testing dexterity in recruitment contexts and for testing and training eye-hand-coordination in neuropsychology. In neuropsychology it helps to assess neurological damages. Our version has the imprint "U.S.E.S. PEGBOARD". The abbreviation stands for "United States Employment Services". We got our exemplar donated though from the psychological laboratory of the Otto Wagner Hospital in Vienna, a psychiatry.
A lot of games that originate from primitive cultures have hand-made wood-sculpted boards, are played with pretty pebbles from the local beach or forest, and have countless variations to the rules (like Mancala). To me this looks like one of those games, but from a somewhat more recent time.
There are infinitely many games you could play on this 12x8 board with double sided pieces, so I hope you have a game in mind but can't remember the title. Here's some guesses:
This is my best attempt at an answer to a question that I fear has no single answer. If you feel that these don't answer your question, please explain in your question why not, and I can delete this answer.
I just did a Massachusetts state assessment test for the local Boston insulators union and this board was given to us to test manual dexterity. The test was broken down into two parts, each 30 seconds long. The first test we had to remove the pegs from one side to the next using both hands, the second test we had to flip the pegs one by one using only one hand.
By the way, the board we used looked exactly like the one posted by Sascha Frank
Although this is a non-standard board size, you could play Pente with this set.
As Bostonian previously stated....
I also took a mechanical aptitude and spacial relations test for a Boston Trades Union (Plumbers and Gasfitters) and as part of the Manual Dexterity portion of the exam, the U.S.E.S. Pegboard was used as the exam was proctored by MA Div. of Career Resources. (following the written portion of the exam)
They used to have games like this at "folksy" restaurants when I was a kid. (The peg board resembles a cribbage-type board, although it's obviously not a cribbage board.)
It might be a proto-version of TwixT, without the strings.
Although it's possible it could be a jumping game, like Konane, I'd be surprised if it was for a jumping game like Halma or Checkers, where a checker board is pretty standard.
The lack of context may be for the purpose of generalization--it is not a single game, but can be used for a variety of connection games and jumping games.
I recently purchased five of these from excess inventory (surplus) sales from a correctional institute. These were used in inmate mental status. I paid $1.00 each for them.
