Answer
$$[x]_S=\left[ \begin {array}{ccc} -1\\ 2\\0\\1\end {array} \right].$$
Work Step by Step
Since we have
$$x= \left(0,0,0,1\right)-2\left(0,0,1,1\right)+3\left(0,1,1,1\right)-(1,1,1,1)=\left(-1,2,0,1\right).$$
then we can write $x$ relative to the standard basis of $R^4$ as follows
$$x= \left(-1,2,0,1\right)=-(1,0,0,0)+2 (0,1,0,0)+0(0,0,1,0)+(0,0,0,1) .$$
Thus, he coordinates matrix of $x$ in $R^4$ relative to the
standard basis is
$$[x]_S=\left[ \begin {array}{ccc} -1\\ 2\\0\\1\end {array} \right].$$
