How to write it? This problem bug me for a long time. Until now, I still don't know...

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This might be a very first start with lots of room for improvement. At least now you can play with different settings for widths and colors.
Here's the code:
\documentclass{article}
\usepackage{enumitem}
\usepackage{xcolor}
\renewcommand{\descriptionlabel}[1]{%
\hspace{\labelsep}%
\colorbox{yellow}{\textbf{#1}}%
\par
}
\newlist{mydescription}{description}{1}
\setlist[mydescription]{
topsep=2ex,
partopsep=2ex,
itemsep=1ex,
font=\bfseries\color{blue},
labelwidth=3em,
labelsep*=2em,
leftmargin =!,
}
\begin{document}
\begin{mydescription}
\item[G1.] The first item
\item[G2.] The second item
A longish explanation every true mathematician would deem completely unnecessary …
\item[G3.] The third item etc …
\end{mydescription}
\end{document}
Here's the output:
phil-elkabat
- 2,055

please do this for meservice. We provide answers to concrete questions. You might want to have a look attikz– daleif Aug 06 '20 at 12:27enumitem-package. There is a lot you can do with description lists. – phil-elkabat Aug 06 '20 at 13:31arabicnumbers. – Sebastiano Aug 06 '20 at 14:10