Two independent vectors U & V will span the set W if you have constants s & t such that:
sU + tV = member of W.
Well lo and behold the general vector in the set W already has s & t constants in its components. So looking at the pattern there, let's try all the coefficients in the s terms for U and the t terms for V:
U = (+2, -2, -2, +3)
V = (- 4, 0, +1, -3)
Then s(+2, -2, -2, +3) + t(-4, 0, +1, -3) = (2s-4t, -2s, -2s +t, 3s - 3t) or the general vector in set W.
So it all works