Try this:
DECLARE @dateEntered date = '2022-03-02';
SELECT DATEADD(qq, DATEDIFF(qq, 0, @dateEntered) - 1, 0) AS First_Date_of_Previous_Quarter,
DATEADD(dd, -1, DATEADD(qq, DATEDIFF(qq, 0, @dateEntered), 0)) AS Last_Date_of_Previous_Quarter,
DATEADD(qq, DATEDIFF(qq, 0, @dateEntered), 0) AS First_Date_of_Current_Quarter,
DATEADD(dd, -1, DATEADD(qq, DATEDIFF(qq, 0, @dateEntered) + 1, 0)) AS Last_Date_of_Current_Quarter;
Please post each table DDL and sample data based on your output from your screenshot (https://docs.microsoft.com/en-us/answers/storage/attachments/196639-422project-2.png). So we can do the test.
Try this: