You're trying to install a package that is not intended for the exact version of the distribution you're using, and so you're hitting dependency problems. Unfortunately, that's normal. That's part of the reason why different distributions and their different major releases exist: to define what library versions can be expected to be available on each major release.
Error: Dependency is not satisfiable: imagemagick-common (=8:220.127.116.11-5+deb8u13) message would seem to indicate that the dependency specifically requires a version that is specific to Debian Jessie (= Debian major release 8).
A later version is already installed suggests you have either a newer release of Debian or one of the Debian-derivative distributions, with a newer major release of ImageMagick in it.
Since ImageMagick is basically a set of libraries and command line tools, many other programs use parts of it and depend on those parts. Now you're trying to have parts of different versions of ImageMagick on the same system; they won't work together. The package management "knows" that and is trying to stop you from doing that.
In essence, you are effectively trying to make a FrankenDebian. Please don't. Or if you persist, consider yourself warned.
From your other question you mentioned in the comments, it appears you're using "Debian buster/sid". So it's a combination of the current testing release (
buster, which is going to be Debian 10 once it becomes stable) and
sid which is the unstable release. Mixing in packages that are 2 major releases older is not a good idea: you should find the appropriate replacements within your current release, and then adapt the scripts of
kde-services if necessary.
kde-services seems to be essentially just a collection of shell scripts and
.desktop files to provide useful functions. The actual functionality is provided by the tools that are specified as its dependencies.
Of those dependencies,
transcode in particular seems problematic: it's apparently been abandoned by its developer, as its website http://www.transcoding.org now only has a single write-up about the care of earbud headphones and nothing else.
Unfortunately the name
transcode isn't very googleable, but I found copies of its source code dating back to year 2014 here and a minor fork of it with some typos fixed in 2018 here.
It would probably be best to try and find another transcoding tool from your current distribution, and adapt the
kde-services scripts to use it instead.
But if you must, instead of using a package intended for Debian 8, you should get
transcode's source code, install any libraries it needs as packages (including the
-dev packages for each of those libraries, for source code compilation!) and then compile
transcode from source. Then it will use the current versions of any libraries it depends on.