Find a basis for $\displaystyle R^4$ includes the vectors: $\displaystyle (1,0,1,0)$ and $\displaystyle (0,1,-1,0)$
Remember a basis is a linear independent spanning set. A Basis of $\displaystyle \mathbb{R}^4$ is going to consist of 4 linear independent vectors. So all you do is take the 2 vectors they gave you and find 2 other linear independent vectors. As Plato suggested just take 2 vectors from the standard basis and see if they are linear independent.