If you want page numbers on the right of the pages use
\cfoot{}
\fancyfoot[RE]{\thepage}
\fancyfoot[RO]{\thepage}
and if you want to make the front and back matter use arabic numbers then just toggle \pagenumbering
as shown:
\documentclass[a4paper,20pt]{book}
\usepackage{fancyhdr}
\usepackage{lipsum}
\usepackage{etoolbox}
\patchcmd{\chapter}{plain}{empty}{}{}
\patchcmd{\part}{plain}{empty}{}{}
\cfoot{}
\fancyfoot[RE]{\thepage}
\fancyfoot[RO]{\thepage}
\begin{document}
\pagestyle{fancy}
\frontmatter
\pagenumbering{arabic}
\chapter{Some figures}
\section{Some section}
\lipsum[1-10]
\mainmatter
\chapter{Some figures}
\section{Some section}
\lipsum[1-10]
\backmatter
\pagenumbering{arabic}
\chapter{Some figures}
\section{Some section}
\lipsum[1-10]
\end{document}