I would need to know what model of shotgun we are talking about before I can say when your browning was made.
What is the value of a 12 gauge Browning shotgun serial J68824?
If you mean a Browning B-2000 12 gauge shotgun then the value would be 495 dollars for a shotgun in the condition you describe.
Use the link below
http://www.browning.com/products
Browning never made a Model 51 shotgun.
100-1000 USD
Need a detailed description
50-700 usd
0-400 usd
250
50-500 usd
100-2000 usd