\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\draw[thin,->] (0,0) -- (9,0) node[above]{$x$};
\draw [thin,->] (0,-4) -- (0,3.3) node[right]{$t$};
\fill[lightgray] (-3,-3)--(0,-3)--(-0,3)--(-3,3);
\draw[thick] (0,-3) --(0,3);
\draw[blue] (0,0) -- (6,3);
\draw[teal] (0,0) -- (6,-3);
\node at (5,0) {\colorbox{yellow}{$u= -2\cos(x+2t)+6\cos(x-2t)$}};
\node at (3.5 ,2.5) {\colorbox{yellow}{$u= -2\cos(x+2t)-6\cos(x-2t)+4$}};
\node at (3,-2.5) {\colorbox{yellow}{$u=2\cos(x+t) +6\cos(x-2t)-4$}};

\end{tikzpicture}
\end{document}