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Ajustar la posición de la etiqueta del nodo en el gráfico

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Ajustar la posición de la etiqueta del nodo en el gráfico

La pregunta es que la posición del nodo (16, 20) se está mezclando con la línea. ¿Cómo deshacerse de esto? Es decir, quiero trazar este nodo en el lado derecho para que no haya posibilidad de colisión con la línea.

Esto es lo que he hecho hasta ahora.

\documentclass[12pt, a4paper]{article}
\usepackage[a4paper,top=1 in,bottom=1 in,left=0.7 in,right=0.7 in]{geometry}
\usepackage[utf8]{inputenc}
\usepackage[misc]{ifsym}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{tikz}
\usepackage{pst-tree}
\usetikzlibrary{intersections}
\begin{document}    
\begin{center}
    \begin{tikzpicture}
\draw[thick,latex-latex] (-1,0) -- (13,0)node[right]{$x$};
\draw[thick,latex-latex] (0,-1) -- (0,13)node[above]{$y$};
\node at (-0.3,-0.3) {};
\foreach \x/\l in {,1/2,2/4,3/6,4/8,5/10,6/12,7/14,8/16,9/18,10/20,11/22,12/24}{
    \node[fill,circle,inner sep=1.5pt,label=below:$\l$] at (\x,0) {};
    \node[fill,circle,inner sep=1.5pt,label=left:$\l$] at (0,\x) {};
}
\draw[thick,stealth-stealth, shorten >= -4cm, shorten <= -1cm,name path =b ](2,4) -- (6,8);
\draw[thick,stealth-stealth, shorten >= -1cm, shorten <= -1.5cm,name path =b ](10,8) -- (6,12);
\foreach \x/\y/\name/\m/\n in {4/6//8/12}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below right:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {2/4//4/8}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below right:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {6/8//12/16}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below :\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {10/8//20/16}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below left:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {8/10//16/20}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below left:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {6/12//12/24}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below left:\name($\m, \n$)}] at (\x,\y) {};
}
\draw (9,11) node[anchor=north west,rotate=0] {$x-y=-4$};
\draw (2.1,13) node[anchor=north west,rotate=0] {$2x-y-2=0$};

\end{tikzpicture}
\end{center}  

\end{document}

Respuesta1

Cambié y cambié belowa 3 puntos en su código:rightinner sep=

\documentclass[12pt, a4paper]{article}
\usepackage[a4paper,top=1 in,bottom=1 in,left=0.7 in,right=0.7 in]{geometry}
\usepackage[utf8]{inputenc}
%\usepackage[misc]{ifsym}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{tikz}
\usepackage{pst-tree}
\usetikzlibrary{intersections}
\begin{document}    
\begin{center}
    \begin{tikzpicture}
\draw[thick,latex-latex] (-1,0) -- (13,0)node[right]{$x$};
\draw[thick,latex-latex] (0,-1) -- (0,13)node[above]{$y$};
\node at (-0.3,-0.3) {};
\foreach \x/\l in {,1/2,2/4,3/6,4/8,5/10,6/12,7/14,8/16,9/18,10/20,11/22,12/24}{
    \node[fill,circle,inner sep=1.5pt,label=below:$\l$] at (\x,0) {};
    \node[fill,circle,inner sep=1.5pt,label=left:$\l$] at (0,\x) {};
}
\draw[thick,stealth-stealth, shorten >= -4cm, shorten <= -1cm,name path =b ](2,4) -- (6,8);
\draw[thick,stealth-stealth, shorten >= -1cm, shorten <= -1.5cm,name path =b ](10,8) -- (6,12);
\foreach \x/\y/\name/\m/\n in {4/6//8/12}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below right:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {2/4//4/8}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below right:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {6/8//12/16}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below right:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {10/8//20/16}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below left:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {8/10//16/20}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=3pt]right:\name($\m, \n$)}] at (\x,\y) {};
}
\foreach \x/\y/\name/\m/\n in {6/12//12/24}{
    \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]below left:\name($\m, \n$)}] at (\x,\y) {};
}

\draw (9,11) node[anchor=north west,rotate=0] {$x-y=-4$};
\draw (2.1,13) node[anchor=north west,rotate=0] {$2x-y-2=0$};

\end{tikzpicture}
\end{center}  

\end{document}

Con el siguiente resultado:

ingrese la descripción de la imagen aquí

Nota adicional de Torbjørn T.: Realmente no veo por qué usas \foreachetiquetas de puntos, en ninguno de los casos recorre varias entradas en una lista. Sin embargo, al agregar una variable de iteración más para la posición, puedes agregar todas las etiquetas con un bucle:

\documentclass[12pt, a4paper]{article}
\usepackage{tikz}
\usetikzlibrary{intersections}
\begin{document}    
\begin{center}
\begin{tikzpicture}
\draw[thick,latex-latex] (-1,0) -- (13,0)node[right]{$x$};
\draw[thick,latex-latex] (0,-1) -- (0,13)node[above]{$y$};
\node at (-0.3,-0.3) {};
\foreach \x/\l in {,1/2,2/4,3/6,4/8,5/10,6/12,7/14,8/16,9/18,10/20,11/22,12/24}{
    \node[fill,circle,inner sep=1.5pt,label=below:$\l$] at (\x,0) {};
    \node[fill,circle,inner sep=1.5pt,label=left:$\l$] at (0,\x) {};
}
\draw[thick,stealth-stealth, shorten >= -4cm, shorten <= -1cm,name path =b ](2,4) -- (6,8);
\draw[thick,stealth-stealth, shorten >= -1cm, shorten <= -1.5cm,name path =b ](10,8) -- (6,12);
\foreach \x/\y/\name/\m/\n/\pos in
  {4/6//8/12/below right,
   2/4//4/8/below right,
   6/8//12/16/below right,
   10/8/\hspace{3pt}/20/16/below left,
   8/10//16/20/right,
   6/12//12/24/below left}
{
 \node[fill,circle,inner sep=2.5pt,label={[inner sep=0pt]\pos:\name($\m, \n$)}] at (\x,\y) {};
}
\draw (9,11) node[anchor=north west,rotate=0] {$x-y=-4$};
\draw (2.1,13) node[anchor=north west,rotate=0] {$2x-y-2=0$};
\end{tikzpicture}
\end{center}  
\end{document}

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