\documentclass[12pt,a4paper,german]{article}
\usepackage{url}
%\usepackage{graphics}
\usepackage{times}
\usepackage[T1]{fontenc}
\usepackage{ngerman}
\usepackage{float}
\usepackage{diagbox}
\usepackage[utf8]{inputenc}
\usepackage{geometry}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{cancel}
\usepackage{csquotes}
\usepackage{graphicx}
\usepackage{epsfig}
\usepackage{paralist}
\usepackage{tikz}
\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}

%%%%%%%%%% Fill out the the definitions %%%%%%%%%
\def \name {Valentin Brandl}					%
\def \matrikel {108018274494}				%
\def \pname {Marvin Herrmann}				%
\def \pmatrikel {108018265436}				%
\def \gruppe {2 (Mi 10-12 Andre)}
\def \qname {Pascal Brackmann}
\def \qmatrikel {108017113834}				%
\def \uebung {6}								%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 % DO NOT MODIFY THIS HEADER
\newcommand{\hwsol}{
\vspace*{-2cm}
\noindent \matrikel \quad \name \hfill \"Ubungsgruppe: \gruppe \\
\noindent \pmatrikel \quad \pname \\
\noindent \qmatrikel \quad \qname \\
\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
}

\begin{document}
%Import header
\hwsol

\section*{Aufgabe 6.1}

\begin{tabular}{|c|ccccccc|}
    \hline
    Stack & $pred[1]$ & $pred[2]$ & $pred[3]$ & $pred[4]$ & $pred[5]$ & $pred[6]$ & $pred[7]$ \\\hline
    $\emptyset$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
    \cancel{1} & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
    1, \cancel{2} & $nil$ & $1$ & $nil$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
    1, 2, \cancel{3} & $nil$ & $1$ & $2$ & $nil$ & $nil$ & $nil$ & $nil$ \\\hline
    1, 2, 3, \cancel{4} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $nil$ & $nil$ \\\hline
    1, 2, \cancel{3} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $nil$ & $nil$ \\\hline
    1, \cancel{2} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $nil$ & $nil$ \\\hline
    1, 2, \cancel{6} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $nil$ \\\hline
    1, 2, 6, \cancel{7} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $6$ \\\hline
    1, 2, \cancel{6} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $6$ \\\hline
    1, \cancel{2} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $6$ \\\hline
    \cancel{1} & $nil$ & $1$ & $2$ & $3$ & $nil$ & $2$ & $6$ \\\hline
    1, \cancel{5} & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
    \cancel{1} & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
    $\emptyset$ & $nil$ & $1$ & $2$ & $3$ & $1$ & $2$ & $6$ \\\hline
\end{tabular}

\end{document}