Sum[((1/3) (-((12 Cos[
                            (1/6) (-1 + 
                                  2 n) π])/((-1 + 
                              2 n) π)) - ((144 Sin[(1/12) (-1 + 2 n) π])/((((-1 + 2 n))^2) (π^2))) + ((144 Sin[(1/6) (-1 + 2 n) π])/((((-1 + 2 n))^2) (π^2)))) + 
            (1/3) (((12 Cos[(1/6) (-1 + 2 n) π])/((-1 + 2 n) π)) + ((144 Sin[(1/6) (-1 + 2 n) π])/((((-1 + 2 n))^2) (π^2))) - ((144 Sin[(1/4) (-1 + 2 n) π])/((((-1 + 2 n))^2) (π^2)))))*
        Sin[(((2*n - 1))/12)*π*x]*Cos[(((2*n - 1))/12)*π*t], {n, 1, 
        100}]
\(Table[
      Plot[Sum[\((1\/3\ \((\(-\(\(12\ Cos[
                                1\/6\ \((\(-1\) + 
                                      2\ n)\)\ π]\)\/\(\((\(-1\) + 
                                  2\ n)\)\ π\)\)\) - \(144\ Sin[1\/12\ \((\(-1\) + 2\ n)\)\ π]\)\/\(\((\(-1\) + 2\ n)\)\^2\ π\^2\) + \(144\ Sin[1\/6\ \((\(-1\) + 2\ n)\)\ π]\)\/\(\((\(-1\) + 2\ n)\)\^2\ π\^2\))\) + 
                1\/3\ \((\(12\ Cos[1\/6\ \((\(-1\) + 2\ n)\)\ π]\)\/\(\((\(-1\) + 2\ n)\)\ π\) + \(144\ Sin[1\/6\ \((\(-1\) + 2\ n)\)\ π]\)\/\(\((\(-1\) + 2\ n)\)\^2\ π\^2\) - \(144\ Sin[1\/4\ \((\(-1\) + 2\ n)\)\ π]\)\/\(\((\(-1\) + 2\ n)\)\^2\ π\^2\))\))\)*
            Sin[\((2*n - 1)\)\/12*π*x]*
            Cos[\((2*n - 1)\)\/12*π*t], {n, 1, 100}], {x, \(-10\), 10}, 
        PlotRange -> {{0, 6}, {\(-1.1\), 1.1}}, 
        AxesLabel -> {"x", "u(x,t)"}, 
        PlotStyle -> {RGBColor[1, 0, 1], Thickness[0.015]}], {t, 0, 12, 
        0.1}]\)