Answer
$(0,6,-8)$
Work Step by Step
In this case the transformation is linear if $T(v_1+v_2)=T(v_1)+T(v_2)$ and $T(av_1)=aT(v_1)$ for any $v_1,v_2$ in the domain and any $a$ scalar.
Hence $T(-2,4,-1)=-2T(1,0,0)+4T(0,1,0)-T(0,0,1)=-2(2,4,-1)+4(1,3,-2)-(0,-2,2)=-(4,8,-2)+(4,12,-8)-(0,-2,2)=(0,6,-8)$