One of many sources: https://linuxconfig.org/amd-radeon-ubuntu-20-04-driver-installation
Ubuntu drivers
The providing package for the driver is xserver-xorg-video-radeon_19.1.0-1_amd64, so you should install it with sudo apt install xserver-xorg-video-radeon_19.1.0-1_amd64 (apt-get is disfavored).
This should work out-of-the-box.
Proprietary drivers
If you want to go with proprietary drivers, there is a simple guide.
Go to the AMD Download Page, and grab the latest version of the drivers that matches your card.
Then execute (with suitable version numbers)
$ tar -xf amdgpu-pro_*.tar.xz
$ cd amdgpu-pro-XX.XX-XXXXXX
$ ./amdgpu-pro-install -y
Third party repository
To have the latest AMD Radeon driver version execute
$ sudo add-apt-repository ppa:oibaf/graphics-drivers
$ sudo apt update && sudo apt -y upgrade
TL;DR:
Ubuntu drivers
From https://help.ubuntu.com/community/BinaryDriverHowto/AMD
NOTE: For Ubuntu 16.04 LTS and above, the AMD Catalyst or fglrx driver
is no longer supported by AMD, or in Ubuntu.{1} If you have an AMD GPU
and wish to run any Ubuntu version 16.04 LTS or newer, there are two
open source driver options: Radeon or AMDGPU. The AMDGPU-PRO driver
provides the open source AMDGPU driver and a proprietary overlay.
Newer AMD GPUs designed with GCN technology (Graphics Core Next)
should use AMDGPU or AMDGPU-PRO, while older AMD GPUs should use
Radeon.
For the graphics card Radeon HD 4350/4550 the chipset is RV710.
According to this official info (or man radeon), that card/chipset is in the list of SUPPORTED HARDWARE by the radeon Xorg driver,
with the following features:
- Full support for 8-, 15-, 16- and 24-bit pixel depths, and for 30-bit depth on Linux 3.16 and later;
- RandR 1.2 and RandR 1.3 support;
- Full EXA 2D acceleration;
- Textured XVideo acceleration including anti-tearing support (Bicubic filtering only available on R/RV3xx, R/RV/RS4xx, R/RV5xx, and RS6xx/RS740);
- 3D acceleration;
The providing package is xserver-xorg-video-radeon_19.1.0-1_amd64, so you should install it with sudo apt install xserver-xorg-video-radeon_19.1.0-1_amd64 (apt-get is disfavored).
This should work out-of-the-box.
The problem you are quoting in the OP is 'libqtgui4' has no installation candidate.
What makes you think you need it to have the right amd drivers for your card?
Where did you get such info/hint?
What about the other packages you are installing?
I suggest you go over the following commands one by one, and post the output in the OP, by copy-pasting text, not screen capture.
That will help solving potential problems in case the solution does not work.
$ sudo update-pciids
$ lspci -nn | grep -E 'VGA|Display'
$ dmesg | egrep -i 'drm|radeon'
$ sudo lshw -c video
$ lsmod | grep amd
$ glxinfo -B
Note: This is perhaps an alternative, YMMV.
