$x(n) = {1, 2, 3, 4, 5, 6, 7, 8 } \ h(n) = {1, 1, 1 } \ \therefore, h(n) = {1, 1, 1, 0} \ x_1(n)= {1, 2, 0, 0} \ x_2(n)= {3, 4, 0, 0} \ x_3(n)={5, 6, 0, 0} \ x_4(n)={7, 8, 0, 0} \
y_1(n) = x_1(n) \otimes h_1(n)$ ![enter image description here][1] $\therefore, y_1$(n) = {1, 2, 3, 2} $y_2(n) = x_2(n) \otimes h_2(n)$ ![enter image description here][2] $\therefore, y_2(n)$ = {3, 7, 7, 4} $y_3(n) = x_3(n) \otimes h_3(n)$ ![enter image description here][3] $\therefore, y_3(n)$ = {5, 11, 11, 6} $y_4(n) = x_4(n) \otimes h_4(n)$ ![enter image description here][4] $\therefore, y_4(n)$ = {7, 15, 15, 8}

Result: y(n) = {1, 3, 6, 9, 12, 15, 18, 21, 15, 8}