You determine the date acquired and the cost basis from your own records of the original purchase.
If you do not have a record of the purchase, the broker, investment manager, or other financial institution that issued the 1099-B might be able to help you determine the date acquired and the cost basis, even though they did not put the information on the 1099-B.
What type of asset or investment did you sell? Was it stock, a mutual fund, or something else? How did you acquire the investment? Did you purchase it yourself, or did you acquire it some other way, such as by gift or inheritance?
If you don't know the exact purchase date, do you have at least a rough idea of when you purchased the investment?
If you cannot come up with any information at all, use your best guess for the date acquired and use zero for the cost basis. The exact date acquired isn't really important. What matters is whether you owned the investment for more than a year, or for one year or less. If you use zero as the cost basis you will have to pay tax on the entire proceeds of the sale, but that's what you're stuck with if you cannot determine the actual cost basis.
You determine the date acquired and the cost basis from your own records of the original purchase.
If you do not have a record of the purchase, the broker, investment manager, or other financial institution that issued the 1099-B might be able to help you determine the date acquired and the cost basis, even though they did not put the information on the 1099-B.
What type of asset or investment did you sell? Was it stock, a mutual fund, or something else? How did you acquire the investment? Did you purchase it yourself, or did you acquire it some other way, such as by gift or inheritance?
If you don't know the exact purchase date, do you have at least a rough idea of when you purchased the investment?
If you cannot come up with any information at all, use your best guess for the date acquired and use zero for the cost basis. The exact date acquired isn't really important. What matters is whether you owned the investment for more than a year, or for one year or less. If you use zero as the cost basis you will have to pay tax on the entire proceeds of the sale, but that's what you're stuck with if you cannot determine the actual cost basis.
See OP's new question with details.