How can I delete a "Free Space" partition!?

First, you need to create a partition that is formatted properly. Free Space is just that - unformatted space. Second, you need to select the free space in order to work with it. When selected that segment will be blue while the rest of circle will turn white. Third, format the free space partition HFS+. Fourth, select the newly formatted volume than click on the Delete [-] button to remove it.

If you are unsuccessful with the above, then you need to Erase the entire drive and reformat from scratch. Be sure you have backed up your files.

In the last image, you have the segment selected. Note that the Delete [-] button is active. Click on the Delete [-] button to remove the smaller partition. If this does not rejoin it to the existing space, then you will need to Erase and Reformat the entire drive or leave the partition as is.

Glad to help. Have a great week. 😀