I am getting warnings that my Filesystem root is running out of space. I have tried a number of things which the internet told me to do, but nothing seems to be solving the problem.
I am running Ubuntu MATE 20.04 with a hard disk (sda) and an SSD (sdb); gparted shows this:

I have very little experience with partitions and such, but it seems to me that if sdb5 could be extended to include what is now sdb6, that would double the space available to the root of mate 20.04.
But, I would like to preserve mate 16.04 if possible. Looking at sda, there is a partition sda9 (called "huge unused") which has way more than enough space for mate 16.04. So my detailed plan is this:
Move the mate 16.04 partition from SSD to hard drive:
Split sda9 (currently 385.51 GiB)) into two partitions of these sizes:
sda9 355.51 GiB
sda10 30.00 GiB
Copy sdb6 (mate 16.04) to sda10.
Change boot options so that 16.04 can still be launched from
its new location.
Increase the space available to mate 20 on the SSD:
Combine the three partitions sdb5, unallocated, and sdb6 into
one partition.
Will this work? And, if so, what I desperately need are detailed instructions on how to execute the plan. My experience with gparted is quite limited.
A secondary question is why mate 20.04 is using 28 GiB while mate 16.04 is using only 14 GiB.
A friend of mine, Mike, set up all the partitions on my system, and normally I would go to him for help. But a few months ago he left the planet, so I am more or less on my own in terms of keeping my system going.
Any help will be greatly appreciated.