Mac OS merge other partition into OS partition without losing data on primary OS partition i have a mac book pro 2015 with 125 ssd drive. bellow is my partition table









my question is how can i merge partition "BackUp" into my "2:                 Apple_APFS Container disk1         71.8 GB    disk0s2" (data on BackUp can be errase but data on OS partition should be preserved). The purpose is to increase the primary OS partition (need some more space for the OS)

I have tried disk Utilities but seem there is no operation support the above desire yet. Any suggestion? Thanks.
Apple does not provide a way to add the space occupied by disk0s4 to disk0s2. To enlarge disk0s2 there must be significant free space directly below the partition. In your case, disk0s3 is below disk0s2 which blocks the possibility of enlarging disk0s2.

You could backup the contents of disk0s2. There does not appear to be enough space anywhere on disk0 to do this. You would have to find addition storage such as a external drive. Once the contents of disk0s2 is backed up, you could remove both disk0s2 and disk0s3. Next, you could enlarge disk0s2 to occupy all the newly create free space. Finally, you could recreate the "Data" volume by either adding a new volume to the APFS container or shrinking disk0s2 while creating a new disk0s3. You could then restore the contents of the "Data" volume from the backup.

I should note that when I stated there was not enough space to backup disk0s2, I did not consider a compress backup of this partition. You could consider trying to make a backup in the form of a dmg file by using the Disk Utility application.