After reflecting the figure across the y-axis, the x-coordinates of the points will change their sign.
Point X, originally at (-4, -3), will end up at (4, -3).
Point Y, originally at (5, -2), will end up at (-5, -2).
Point Z, originally at (6, 6), will end up at (-6, 6).
Point W, originally at (-2, 1), will end up at (2, 1).
Out of these options, only Point Z (now at (-6, 6)) will end up in Quadrant I.