The partition table on my machine is MBR and it looks like this:
sda4 (extended)
-sda5 - 1000MB /boot for Ubuntu Desktop 18.04 - ext4
-sda6 - 1000MB not used - ext4
-sda7 - 1000MB not used - ext4
-sda8 - 30GB / for Ubuntu 18.04 Desktop - ext4
-sda9 - 30GB not used - ext4
-sda10 - 30GB not used - ext4
-sda11 - 12GB swap
-sda12 - 700GB /home - ext4
As you can see I have already successfully installed Ubuntu 18.04 Desktop. Partitions were made with GParted when installing Ubuntu 18.04 from a live USB. When I try to install Ubuntu Server 18.04, at the stage of selecting partitions, when I select the 9th partition, the installation process crashes every time.
This is how the report looks :
Even though the date shown in your screen capture would not support this, you might require the accepted solution in Ubuntu 18.04 Installer crashes on Dell XPS 15 9560 (related: Installer crashed when trying to install Ubuntu 18.04).
I wouldn't think you are experiencing Ubiquity install wizard crashes; cannot install ubuntu-MATE 18.04.4.
Related: