problem.tex

\documentclass{report}
\usepackage{amsmath}
\begin{document}
\[
\left\{
\begin{alignedat}{2}
&\left.\begin{aligned}
1+4+3\\ 1+3+4
\end{aligned} \right\} &= 5
\\
&\left.\begin{aligned}
1+2+1\\ 1+1+2
\end{aligned} \right\} &= 8
\end{alignedat}
\right.
\]
\end{document}