Unable to delete/resize partition with DiskUtility
The pie chart used by the Disk Utility application can give an user the impression that partitions are stored in some sort of circular fashion. Actually, partitions are store linearly. The output from the command diskutil list will shows this. Also, this output will show partitions that can be hidden when viewing the contents of a drive with the Disk Utility application. Most likely your drive is arranged with the Backup HD partition occurring before the EXT HD partition. In this case, macOS offers no effective way to merge the space from the Backup HD partition into the EXT HD partition. One solution would be to backup the data on the EXT HD partition, create one large partition, then restore from the backup.
There exists third party tools which can do what you are asking in your question, but before using such a tool, you should backup your data. However, once backed up there is no need to use the third party tool.