I need a layout like this on a single page without any other text or floats.
| figure 1a | figure 1b |
Caption for Figure 1
| figure 2a | figure 2b |
Caption for Figure 2
Do anyone know what to do with it?
I need a layout like this on a single page without any other text or floats.
| figure 1a | figure 1b |
Caption for Figure 1
| figure 2a | figure 2b |
Caption for Figure 2
Do anyone know what to do with it?
If you're not interested in separate sub-captions for each of the sub-figures, then you can get away with only the following:

\documentclass{article}
\usepackage{lipsum,graphicx,afterpage}
\begin{document}
\lipsum[1-3]
\afterpage{\clearpage}% To make sure the image appears on the following page
\begin{figure}[p]
\centering
\null\hfill%
\includegraphics[width=.3\linewidth]{example-image-a}%
\hfill%
\includegraphics[width=.3\linewidth]{example-image-b}%
\hfill\null%
\caption{This is the first figure}
\null\hfill%
\includegraphics[width=.3\linewidth]{example-image-b}%
\hfill%
\includegraphics[width=.3\linewidth]{example-image-a}%
\hfill\null%
\caption{This is the second figure}
\end{figure}
\lipsum[4-10]
\end{document}
\hfills stretches out the space beside each sub-float, similar to what is achieved in Reduction of space between two sub-figures (with \hspace*{\fill}).
If you want sub-captions as well, then you need to include a package that provides that functionality. Here's one such implementation using the subcaption package:

\usepackage{subcaption}
%...
\begin{figure}[p]
\centering
\null\hfill%
\subcaptionbox{sub 1a}
{\includegraphics[width=.3\linewidth]{example-image-a}}%
\hfill%
\subcaptionbox{sub 1b}
{\includegraphics[width=.3\linewidth]{example-image-b}}%
\hfill\null%
\caption{This is the first figure}
\null\hfill%
\subcaptionbox{sub 2a}
{\includegraphics[width=.3\linewidth]{example-image-b}}%
\hfill%
\subcaptionbox{sub 2b}
{\includegraphics[width=.3\linewidth]{example-image-a}}%
\hfill\null%
\caption{This is the second figure}
\end{figure}
Other options (with a slightly different interface) would be to use subfig (not the obsolete subfigure).