I think it is clearer if you write if out like this (à la gary above): The set, namely $W$ consists of all points $(w,x,y,z)$ in $\mathbb{R}^4$ such that
$ \left[\begin{array}{c} w\\ x\\ y\\ z\end{array}\right]=s\left[\begin{array}{c} 2\\ 1\\ 0\\ 1\end{array}\right]+t\left[\begin{array}{c} -1\\ 0\\ 1\\ 0\end{array}\right]$.
À la Mark Bennet, you need to check that this linear system above is consistent for every L.H.S. Big hint: consider the matrix formed by the two vectors above as columns, namely the matrix:
$\left[\begin{array}{cc} 2 & -1\\ 1 & 0\\ 0 & 1\\ 1 & 0\end{array}\right]$
At most how many pivot positions can I have when the matrix above is in reduced row echelon form? What does this mean?
Also, what's so special about the vectors in the system, they have 0's and 1's in there, so how do you know just by these 0's and 1's in there that the two vectors are linearly independent?