Write the four equations to the left, then work them out one by one following the four steps:
b-2c=a =>-2c=a-b=-6-(-2)=-4 =>c=2 (third step)
a-2d=c =>-2d=c-a=2-(-6)=8 =>d=-4 (4th step)
4-2a=16 =>a=-6 (first step)
a-2b=b =>3b=-6 =>b=-2 (second step)
so the answer is the first choice.