Convolution of two sets
If it is difficult for you to remember or calculate the convolution of two sequences then you may try doing it as polynomial multiplication. 
Think of x[n] and h[n] as polynomial coefficients. So we have 
Px = 3x^2 + 2*x + 1
Ph = 1x^2 - 2*x + 3

Remember that linear convolution of two sequences is polynomial multiplication. Therefore 
Py = Px * Ph
Py = (3x^2 + 2*x + 1) * (1x^2 - 2*x + 3)
Py = 3x^4 + 2x^3 - 6x^3 + x^2 + 9x^2 - 4x^2 + 6x - 2x + 3
Py = 3x^4 - 4x^3 +6x^2 + 4x + 3

Now writing the polynomial coefficients back in sequence format 
y[n] = {3, -4, 6, 4, 3}