First, you have to prove that the 0 element, aka (0,0,0,0) is in the subspace. This is trivial.

Second, show that if is in the subspace, then is in the subspace. You can try this by substitution. (Hint - seperate out the cases where is positive and negative)

Finally, show that if and are in U, the their sum, is in U. This can also be done by substitution.

If my intuition is correct, then the first one will be a subspace, and the second will not.