Without TikZ, only \colorboxes.
I've added \usepackage{picture} to use the widths/lengths not specified in multiples of \unitlength.
I've added \usepackage{calc} for convenience, to do calculations in \setlength (you can avoid it if you use \addtolength).
I've used \makebox(\myxxxwidth, \myxxxheight){...} to specify the width and total height of the boxes.
I've calculated the width of the boxes this way:
width of the border + width of the content + width of the border
that is
width of the content + double of the width of the border
You can set the border widths as you like.
The same for heights.
I've created a new command \mybox for convenience, you can even modify it to set the border widths as a parameter/parameters, if you like.
\documentclass[pdftex,dutch]{article}
\usepackage{babel}
\usepackage{xcolor}
\usepackage{picture}% see here: https://tex.stackexchange.com/a/48238/101651
\usepackage{calc}
\newlength{\mygraywidth}
\newlength{\mygrayheight}
\newlength{\myyellowwidth}
\newlength{\myyellowheight}
\newlength{\myredwidth}
\newlength{\myredheight}
\newlength{\myblackwidth}
\newlength{\myblackheight}
\definecolor{lichtgrijs}{RGB}{232,232,232}
\definecolor{DE.rood}{RGB}{222,0,0}
\definecolor{DE.geel}{RGB}{255,207,0}
\newcommand{\mybox}[1]{%
\setlength{\mygraywidth}{\widthof{#1}+4mm}
\setlength{\mygrayheight}{\totalheightof{#1}+4mm}
\setlength{\myyellowwidth}{\mygraywidth+1mm}
\setlength{\myyellowheight}{\mygrayheight+1mm}
\setlength{\myredwidth}{\myyellowwidth+1mm}
\setlength{\myredheight}{\myyellowheight+1mm}
\setlength{\myblackwidth}{\myredwidth+1mm}
\setlength{\myblackheight}{\myredheight+1mm}
\colorbox{black}{\makebox(\myblackwidth,\myblackheight){%
\colorbox{DE.rood}{\makebox(\myredwidth,\myredheight){%
\colorbox{DE.geel}{\makebox(\myyellowwidth,\myyellowheight){%
\colorbox{lichtgrijs}{\makebox(\mygraywidth, \mygrayheight){%
#1}}%
}}%
}}%
}}%
}
\begin{document}
\mybox{Vliegtuig}
\vspace{4ex}
\mybox{Do you like it?}
\end{document}

picwith a tiny bit of extra effort you could make the thing rotatable, which the other answers could not (unless one wants to addrotate fitover and over). – Mar 03 '19 at 23:24