Your question can't be answered without a detailed description of ALL markings, finish, overall condition, type of action, barrel length, wood, accessories, box, papers, engraving, etc..
What is the value of a 12 gauge Browning shotgun serial J68824?
$350
1943 browning light 12 belguim made $5K
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.
Basically impossible to value a weapon with just the gauge and sn.
Browning Citori 12 gage over and under & a Browning Goldtrigger Light Twelve: How much are they worth?
Browning never made a Model 51 shotgun.
The value of a 12 gauge Browning Citori Pigeon Grade is actually dependent upon a number of factors. Some of these factors would be the age and condition.
100-500 USD
50-500 usd
100-600 USD
0-400 usd