In my previous answer, I used only the circle to divide the square plate of chocolate into four equal pieces. In this answer, I show how to divide it equally using only the Y shaped thingy.
The general idea is to use thingy to make four long cuts toward the center, each identical relative to its side of the square; and then make two slices across the short gaps to complete the cutting.
Part 1, Mark midpoints of sides:
On each side of the square, place thingy with one post-end in a corner, and the Y-junction clockwise (of that corner) on the side. [See first diagram.] At each placement, mark the Y-junction location (ie, the midpoint of the side).
Part 2, Make four long cuts toward the center:
On each side of the square, place one thingy post-end at the side's mid-point mark, and another post-end against the counterclockwise adjacent side. [See second diagram.] Cut from the mid-point's post-end up to the Y-junction. [Net result is as shown in third diagram.]
Part 3, Make two slices across the short gaps to complete the cutting:
Make two short cuts across the plate-center to connect the ends of opposite long cuts, as shown in red in the fourth diagram, using any leg of thingy as a straightedge.
Edit: A slight variation of this method allows cutting the large square into four equal small squares (instead of shapes with six edges each) using only the 3-leg thingy. Rather than making the long cuts shown in green in the fourth diagram, just mark their endpoints near the center,and make the red lines as marks also. Their intersection marks the center of the plate. Now use a thingy leg as a straightedge to cut from each side's midpoint to the center.