In order for the area of triangle XYD to be at most 12, the height of triangle XYD is at most 2. The height of triangle XYD can be 6, so the probability is 2/6 = 1/3.
Since PQRS is a trapezoid, arcs PS and QR are equal, which leads to the quadratic y^2 + 4y - 60 = 0. The solutions are y = 6 and y = -10, so we take y = 6. Then arcs PS and QR are both 78, so arc PTQ is 360 - 78 - 78 = 202 degrees.