documentclass{article}
usepackage{standalone}
usepackage{tikz}
begin{document}
    begin{tikzpicture}
        draw [->] (0, 0) -- (5, 0) node [right] {$X$};
        draw [->] (0, 0) -- (0, 3) node [above] {$Y$};

        draw [domain=0.66:4.5, thick, blue] plot (x, {2/x});
        draw [domain=1.66:4.5, thick, blue] plot (x, {6/x});

        draw [red, ultra thick] (3, 2) edge [bend right=10] (3.5, 0.57);
        draw [red, ultra thick] (2, 3) edge [bend right=10] (2.5, 0.8);

        draw [domain=2.5:3.5, ultra thick, red] plot (x, {2/x});
        draw [domain=2:3, ultra thick, red] plot (x, {6/x});

        node [above] at (2, 3) {$C$};
        node [below] at (2.5, 0.8) {$B$};
        node [above] at (3, 2) {$D$};
        node [below] at (3.5, 0.57) {$A$};
    end{tikzpicture}
end{document}