You can have figure information saved in the same place as the tables, and hence output at the same time, by adding the following lines in your preamble:
\makeatletter
\def\ext@figure{lot}
\makeatother
\renewcommand*\listtablename{List of Figures and Tables}
Here is a minimal working example:
\documentclass{article}
\makeatletter
\def\ext@figure{lot}
\makeatother
\renewcommand*\listtablename{List of Figures and Tables}
\begin{document}
\listoftables
\clearpage
\begin{figure}
\caption{A picture}
\end{figure}
\begin{table}
\caption{Numbers}
\end{table}
\begin{figure}
\caption{Another picture}
\end{figure}
\end{document}
Output

If you want that list exactly as in your example, load the tocloft
package and add the following lines in your preamble
\renewcommand{\cftfigpresnum}{Figure~}
\renewcommand{\cftfigaftersnum}{:}
\setlength{\cftfignumwidth}{5.5em}
\renewcommand{\cfttabpresnum}{Table~}
\renewcommand{\cfttabaftersnum}{:}
\setlength{\cfttabnumwidth}{5.5em}
MWE
\documentclass{article}
\usepackage{tocloft}
\makeatletter
\def\ext@figure{lot}
\makeatother
\renewcommand*\listtablename{List of Figures and Tables}
\renewcommand{\cftfigpresnum}{Figure~}
\renewcommand{\cftfigaftersnum}{:}
\setlength{\cftfignumwidth}{5.5em}
\renewcommand{\cfttabpresnum}{Table~}
\renewcommand{\cfttabaftersnum}{:}
\setlength{\cfttabnumwidth}{5.5em}
\begin{document}
\listoftables
\clearpage
\begin{figure}
\caption{A picture}
\end{figure}
\begin{table}
\caption{Numbers}
\end{table}
\begin{figure}
\caption{Another picture}
\end{figure}
\end{document}
Output
