k = 1
a = ((-48)/((((2  n - 1)*π))^2))*(Sin[(((2  n - 1)*π)/4)] - 2*Sin[(((2  n - 1)*π)/6)] + 
            Sin[(((2  n - 1)*π)/12)])
u[x_] := (∑_(n = k)^k)(Sin[(((2  n - 1)*π*x)/12)]*(a*
                Cos[(((2  n - 1)*π*t)/12)]))
Table[
      Plot[u[x], {x, -18, 36}, 
        PlotStyle -> {RGBColor[1, 0.7, 0], Thickness[0.015]}, 
        PlotRange -> {{0, 6}, {-0.3, 0.3}}], {t, 0, 24, 
        1}]