The answer is option 2: reflected across the y axis 1 unit down, 1 unit left.
The equation should read y=-2(x+1)-1? The brackets are not shown in the question so are assumed. (Otherwise the question has y=-2x+1-1=-2x.
First reflect the graph using the y axis as a mirror. That gives us y=-2x, reflected across the y axis.
If we move the graph 1 unit up (y more positive) we have the graph of y=-2x+1; 1 unit down (y more negative) is y=-2x-1.
If we move the graph 1 unit to the right (x more positive) we have the graph of x=(-y/2)+1 or y=-2(x-1); 1 unit to the left (x more negative) x=(-y/2)-1 or y=-2(x+1).
If we combine these to make y=-2(x+1)-1 we have 1 unit down and 1 unit to the left. This puts the "origin" at (-1,-1).