Value is too difficult to be accurate without seeing the gun. Condition which includes the amount of original finish and original configuration will determine value. Condition and age is also a factor. Recommend taking it to a gun shop for appraisal. You can also do your own investigation by looking at other models being sold that are in the same condition as yours. Try the gunbroker.com or a periodical called "The Gun List" You can also reference the Blue Book of Gun Values which can be purchased on line at various retailers.
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.
To my Knowledge Browning or for that matter any gunmaker has never made a 16 gauge shotgun with a 4in.chamber.In order to get the answer that you seek,you will need to include the model of Browning shotgun in question along with the serial number(to date the year of manufacture) and the overall condition of your shotgun.
http://www.browning.com/products
Use the link below
Browning never made a Model 51 shotgun.
100-1000 USD
Need a detailed description
50-700 usd
0-400 usd
50-500 usd
100-2000 usd