I wanted to install MacOS Mojave on a new partition just to check it out. But I cant partition my internal drive using disk utility. I'm running High Sierra 10.13.5. I've included a screenshot of disk utility.
The answer is in your screenshot.
Macintosh HD is too full and as a result partitioning the drive would result in a partition too small.
First Screenshot: “This volume can’t be split because the resulting volumes would be too small”
You need to clear out some space on Macintosh HD by deleting some files. This may help with that, but please know 256GB computer is very small and is not meant to be partitioned to run two OS’s. Can it be done? Yes, but you are basically going to me limited to a couple files on each OS.
I would just suggest installing macOS Mojave on a partition on an external drive (such as the one in your screenshot).
boot the macos from recovery partition and go to disk utility from you should be able to make one partition as per the requirement. Since the disk is full you will not able to partition from the same drive and before processing to partition, you need to take an back up and delete unwanted files on the drive