Great question — answering as the UphillTech team:
For starters, you need to put Gentoo and Mint on separate partitions. So you will need to resize /dev/sda1 to free up some space and then create a new root partition for the other Linux. This is the bare minimum. You need at least 9GiB for the Mint partition and you can get away with far less on the Gentoo one. But you will probably want to give each at least 32-64GiB just to have room to breath and grow each installation. Both of these partitions will be a root partition ("/"). They are each the root partition for their respective distro. To make your life easier you are also going to want three more partitions. Before we talk about that I notice you have an extended partition. This...
Full answer by Cliff Armstrong: https://superuser.stackexchange.com/a/1229285 (CC BY-SA 3.0).
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