How to wrap a long equation in Latex

Use aligned:

\begin{equation*}
  \begin{aligned}
    m_{12}(\{ \emph{Red},\emph{Blue} \}) 
    = K' * \bigl[ & m_{1}(\{ \emph{Red},\emph{Blue} \})*m_{2}(\{    \emph{Red},\emph{Blue} \}) \\
     + & m_{1}(\{ \emph{Red},\emph{Blue} \})*m_{2}(\{ \emph{Red},\emph{Blue},\emph{Green} \}) \\
     + & m_{2}(\{ \emph{Red},\emph{Blue} \})*m_{1}(\{ \emph{Red},\emph{Blue},\emph{Green} \})\bigr]
  \end{aligned}
\end{equation*}

Have you tried using the align environment?

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align*}
  m_{12}(\{Red,Blue\})&=K'*[m_1 (\{Red,Blue\})*m_2(\{Red,Blue\})\\
                      &\qquad +m_1(\{Red,Blue\})*m_2(\{Red,Blue,Green\})\\
                      &\qquad +m_2(\{Red,Blue\})*m_1(\{Red,Blue,Green\})]
\end{align*}

\end{document}