You would have to estimate the date acquired from your own records or recollection; the IRS only needs to know if you held the security for mare than a year before selling it
If you acquired the security more than a year before you sold it, you can enter 01/01/2015. This will identify the transaction as "Long-term".
If you acquired the security less than a year before you sold it, you can enter 01/01/2016. This will identify the transaction as "Short-term".
