You can use the following syntax in DAX to filter a table for rows where a date column is between two specific dates:
filtered_data = CALCULATETABLE ( 'my_data', DATESBETWEEN ('my_data'[Date], DATE(2022, 5, 1), DATE(2023, 8, 20)) )
This particular example creates a new table named filtered_data that contains only the rows from the table named my_data where the date in the Date column is between 5/1/2022 and 8/20/2023.
The following example shows how to use this syntax in practice.
Example: How to Filter Between Two Dates in Power BI
Suppose we have the following table in Power BI named my_data that contains information about sales made on various dates at some company:

Suppose we would like to filter the table to only show the rows where the date in the Date column is between 5/1/2022 and 8/20/2023.
To do so, click the Table tools tab and then click the New table icon:

Then type the following formula into the formula bar:
filtered_data = CALCULATETABLE ( 'my_data', DATESBETWEEN ('my_data'[Date], DATE(2022, 5, 1), DATE(2023, 8, 20)) )
This will create a new table named filtered_data that contains only the rows from the table named my_data where the date in the Date column is between 5/1/2022 and 8/20/2023:

To filter using two different dates, simply change the start and end dates within the DATESBETWEEN function in the formula.
Note: You can find the complete documentation for the DATESBETWEEN function in DAX here.
Additional Resources
The following tutorials explain how to perform other common tasks in Power BI:
Power BI: How to Use “If Contains” Formula
Power BI: How to Count Distinct Values with Filter
Power BI: How to Create Measure with Multiple Filter Conditions