\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{braids}

\begin{document}
\begin{tikzpicture}[scale=0.4, every node/.style={scale=0.4}]
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 6,
  braid/strand 2/.style={red},
  braid/strand 5/.style={blue},
  name prefix=braid,
] at (-0.25,0) {braid={
s_4^{-1}
s_3^{-1}
s_2^{-1}s_2^{-1}
s_3
s_4
}};
\node at (-0.7,1) {\fontsize{25pt}{\baselineskip}\selectfont $i$};
\node at (-0.7,4) {\fontsize{23pt}{\baselineskip}\selectfont $j$};
\node at (7.5,2.5) {\fontsize{40pt}{\baselineskip}\selectfont $=$};
\begin{scope}[shift={(9,0)}]
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 6,
  braid/strand 2/.style={red},
  braid/strand 5/.style={blue},
  name prefix=braid,
] at (-0.25,0) {braid={
s_2-s_4^{-1}
s_3^{-1}s_3^{-1}
s_2^{-1}-s_4
}};
\node at (5.5,2.5) {\fontsize{40pt}{\baselineskip}\selectfont $=$};
\begin{scope}[shift={(7,0)}]
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 6,
  braid/strand 2/.style={red},
  braid/strand 5/.style={blue},
  name prefix=braid,
] at (-0.25,0) {braid={
s_2
s_3
s_4^{-1}s_4^{-1}
s_3^{-1}
s_2^{-1}
}};
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document}