Some licenses depending on issue date don't have these document numbers on them. Review the information below first to double check, but if you do not have a document number, then you can continue without actually entering any of the license information (leave it all blank, not just the document number). Or, there will be an option on the screen before to choose no ID. You can select this option in these cases.
Your return will still be processed without it as the IRS does not require the license number and neither does NY, but they are asking for it more of an identity protection measure (some states like Alabama and Illinois are requiring it).
Double check using this information first - the document number is an 8 or 10 digit alphanumeric number found either on the back of the license or lower right hand corner (depending on the year of your license). It is not the same as the drivers license number. I have included a link to the NY authority that displays images below.