Clear[f]
f[x_] := 
      If[1 ≤ x ≤ 3, 1, 0]
u1[x_] := 
      If[(0 ≤ x ≤ 6 && x - t ≥ 0 && 
            x + t ≤ 6), (1/2) (f[x + t] + f[x - t]), 
        0]
u2[x_] := 
      If[(0 ≤ x && x - t <= 0 && 
            x + t <= 6), (1/2) (f[x + t] - f[-x + t]), 
        0]
u3[x_] := 
      If[(x ≤ 6 && x - t ≥ 0 && 
            x + t >= 6), (1/2) (f[x - t] - f[12 - (x + t)]), 
        0]
u4[x_] := 
      If[(x - t <= 0 && x + t ≥ 6 && x + t <= 12 && 
            x - t ≥ -6), ((-1)/2) (f[
                12 - (x + t)] + f[-x + t]), 
        0]
u5[x_] := 
      If[(0 ≤ x && x - t ≤ -6 && 
            x + t ≤ 12), ((-1)/2) (f[12 - (x + t)] - 
              f[12 - (-x + t)]), 0]
u6[x_] := 
      If[(x ≤ 6 && x - t ≥ -6 && 
            x + t ≥ 12), ((-1)/2) (f[-x + t] - 
              f[-12 + (x + t)]), 0]
u7[x_] := 
      If[(x - t ≤ -6 && x + t ≥ 12 && 
            x + t <= 18 && 
            x - t ≥ -12), (1/2) (f[
                12 - (-x + t)] + f[-12 + (x + t)]), 
        0]
g[x_] := 
      u1[x] + u2[x] + u3[x] + u4[x] + u5[x] + u6[x] + 
        u7[x]
Table[
      Plot[g[x], {x, -1, 7}, 
        PlotStyle -> {RGBColor[1, 0.7, 0], Thickness[0.015]}, 
        PlotRange -> {{0, 6}, {-1.1, 1.1}}], {t, 0, 12, 
        0.1}]