Answer
$$[x]_S=\left[ \begin {array}{ccc} 14\\ -11\end {array} \right].$$
Work Step by Step
Since we have
$$x= -2( -1,4)+3(4,-1)=(14,-11).$$
then we can write $x$ relative to the standard basis of $R^2$ as follows
$$x= (14,-11)=14(1,0)-11(0,1) .$$
Thus, he coordinates matrix of $x$ in $R^2$ relative to the
standard basis is
$$[x]_S=\left[ \begin {array}{ccc} 14\\ -11\end {array} \right].$$