What you are doing looks a little funny to me. It looks like you created a partition named "Free space."
What you need to do is arrange the partitions on the drive so that you have
not allocated the space that you want to expand your existing partition into. Typically, the partition you are expanding has to be adjacent to the free space you are adding to it.
If your partition is not adjacent to the free space, Windows is able to perform non-adjacent free space addition if the disk is dynamic instead of simple, which is probably of no use to you since it can't be done on boot disks, and I have no idea the Linux support for such a drive type.
The other option would be to use a partitioning program that supports moving things around for you. It should rearrange things so your partition is in one piece after it finishes.
I haven't used GPARTED in a while so don't remember if it will rearrange the free space or not, but there shouldn't be anything preventing doing the rearranging manually yourself.
Here is another partitioning tool that offers a free version, if you can't get your results with GPARTED:
MiniTool Partition Wizard
Looks like, if you delete the "New Partition #1," slide SDA5 over to the left, adjacent to SDA4, you should then be able to expand SDA6 into the now unallocated free space.