You may need to enter something in the box. If this is not filled in for the date acquired or the cost, you will need to figure out the amounts.
But if nothing is reported to the IRS on this box, what would I put in there?
The box is blank on the 1099-B because the brokerage or financial institution does not have the information. But it's a required entry on your tax return. You have not said which box is blank on your 1099-B. In order to help you with what to put in the box, we need to know which box it is. If the transaction is anything other than a straightforward sale of a security that you owned, also describe the nature of the transaction.
Both the short term transaction and the long term transaction are blank on box (1b) under the date acquired. I have no clue when they were acquired as this is my parents taxes. Neither one of them would know as they both have dementia.
First ask the broker if they have any information about the acquisition dates. Sometimes they have the information, even though they don't put it on the 1099-B. The fact that the broker classified some of the sales as short-term and some as long-term suggests that they know something about when the investments were acquired. Short-term means that the investment was acquired no more than a year before it was sold, so the broker should certainly know about those.
If you can't get any information from the broker, you can enter the word "Various" for the date acquired instead of an actual date. Or you can use your best guess as to the date. The actual date isn't critical, as long as it's consistent with whether the sale was short-term or long-term.
Maybe you can also dig around in your parents' papers. They might have kept some confirmations or other records of stocks that they bought.