How can you find the model number and the year of manufacture and the value of a 12 gauge Ithaca side-by-side serial 234446?

Manufactured in 1913; model should be a Flues or NIG (New Ithaca Gun), as either could have had that serial number. Value depends on condition and how badly someone wants to buy it. 12 GA is more common than 16 or 20, so is worth less. Ballpark is probably in the $350 range. Watch for a little while and see what similar guns are bringing at auction.