\documentclass{article}
\usepackage{amsmath}
\usepackage{hyperref}
\makeatletter
\@addtoreset{figure}{section}
\typeout{\meaning\thefigure}
\typeout{\meaning\theHfigure}
\numberwithin[\Roman]{table}{section}
\typeout{\meaning\thetable}
\typeout{\meaning\theHtable}
\makeatother
\begin{document}
\section{Hello}
  \begin{figure}
    \caption{Hello figure}
  \end{figure}
  \begin{table}
  \caption{Hello table}
  \end{table}
\section{World}
  \begin{figure}
  \caption{Word figure}
  \end{figure}
  \begin{table}
  \caption{Word table}
  \end{table}
\end{document}